7 min read
How to Solve Quadratic Equations: 3 Methods with Examples
Learn how to solve quadratic equations using the quadratic formula, factoring, and completing the square. Step-by-step worked examples with clear explanations.
Step-by-step tutorials with worked examples, formulas, and links to our free calculators.
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Learn how to solve quadratic equations using the quadratic formula, factoring, and completing the square. Step-by-step worked examples with clear explanations.
Learn how to find the slope of a line using the slope formula, rise over run, and slope-intercept form. Covers parallel and perpendicular slopes with worked examples.
Master probability calculations with clear explanations of basic probability, conditional probability, independent events, and combinations. Includes real-world worked examples.
Learn how to calculate percentages step by step. Covers the core formula, percentage increase and decrease, finding a percentage of a number, and common mistakes to avoid.
Master differentiation with this guide to derivative rules. Covers the power rule, product rule, quotient rule, and chain rule with step-by-step KaTeX examples.
Understand standard deviation from the ground up. Learn the difference between population and sample standard deviation with a full worked example using a real dataset.
Learn the compound interest formula A = P(1 + r/n)^(nt) with three fully worked examples. Understand how compounding frequency affects your returns.
Learn what z-scores mean, how the bell curve works, and how to use z-score tables. Includes worked examples and links to our standard deviation calculator.
Master three methods for solving systems of linear equations: substitution, elimination, and matrices. Step-by-step worked examples for each approach.
Master logarithms from the basics to advanced rules. Covers log properties, change of base formula, and real-world applications in science and finance.
Learn multiple methods for calculating triangle area and perimeter, including base times height, Heron's formula, and trigonometric methods with worked examples.
Learn what eigenvalues and eigenvectors are, how to compute them for 2x2 and 3x3 matrices, and why they matter in data science and engineering.
Learn how integrals work, from basic antiderivatives to definite integrals. Covers the power rule for integration, substitution, and the Fundamental Theorem of Calculus.
Learn how to evaluate limits using direct substitution, factoring, rationalisation, and L'Hopital's rule. Covers one-sided limits and limits at infinity.
Understand Taylor and Maclaurin series from scratch. Learn the formula, compute series for common functions, and see how they are used in science and engineering.
Master matrix operations including addition, scalar multiplication, matrix multiplication, determinants, and inverses with step-by-step examples.
A complete guide to fraction arithmetic. Learn how to find common denominators, simplify fractions, and perform all four operations with worked examples.
Learn exponent rules including the product rule, quotient rule, power rule, and negative exponents. Covers scientific notation and real-world applications.
Understand the most important probability distributions: normal, binomial, Poisson, and uniform. Learn when to use each and how to calculate probabilities.
Learn how to convert between metric and imperial units for length, mass, temperature, and more. Includes dimensional analysis and conversion factor tables.
Learn how to work with ratios and proportions, including simplification, cross multiplication, direct and inverse proportion, and real-world applications.
Learn about complex numbers from basics to advanced topics. Covers arithmetic, polar form, Euler's formula, De Moivre's theorem, and applications in engineering.
Understand the difference between permutations and combinations. Covers factorials, the counting principle, Pascal's triangle, and probability applications.
Learn how to find the greatest common divisor and least common multiple using prime factorisation, the Euclidean algorithm, and their key relationship.
Learn how to compute partial derivatives, understand the gradient vector, and apply multivariable calculus to optimisation, physics, and economics with worked examples.
Master series and summation from arithmetic and geometric series to convergence tests. Covers sigma notation, telescoping series, power series, and practical applications.
Learn how to calculate percentage change, percentage increase, percentage decrease, and percentage difference. Covers successive changes, reverse problems, and common pitfalls.
Learn the Pearson correlation coefficient, simple linear regression, the least squares method, and R-squared. Full numerical examples and common pitfalls explained.
Understand how compound interest works with the core formula, simple vs compound comparisons, monthly contributions, loan calculations, and the Rule of 72.
Master the quadratic formula with tips on the discriminant, graphing parabolas, Vieta's formulas, and real-world applications in physics, economics, and engineering.
A complete guide to fundamental statistics. Covers mean, median, mode, range, variance, standard deviation, IQR, z-scores, and when to use each measure.
Speed up your fraction calculations with the butterfly method, cross-cancellation, the benchmark method, and quick conversion tricks. Practical shortcuts with examples.
See how slope applies beyond the classroom in road engineering, economics, medicine, meteorology, physics, and population growth. Worked examples for each application.
Every exponent rule in one place: product, quotient, power of a power, zero, negative, and fractional exponents. Quick-reference formulas, worked problems, and common mistakes.
Learn the key integration techniques including substitution, integration by parts, partial fractions, and trigonometric substitution with worked examples.
Discover how matrices power real-world applications in computer graphics, machine learning, Google PageRank, economics, cryptography, and quantum computing.
See how probability influences everyday decisions from weather forecasts and medical tests to insurance, games, and investing. Practical examples with calculations.
Speed up your unit conversions with practical tips, mental shortcuts, and tricks for metric/imperial, temperature, speed, and cooking measurements.
A complete introduction to trigonometry covering sine, cosine, tangent, the unit circle, radians, Pythagorean identity, angle addition formulas, and the laws of sines and cosines.
Learn what differential equations are, how to classify them, and how to solve first-order ODEs using direct integration, separation of variables, and integrating factors.
Learn the coefficient of variation formula (CV = σ/μ × 100), when to use CV vs standard deviation, and how to compare variability across datasets with different units.
Learn how to perform chi-square goodness of fit and independence tests. Covers the formula, degrees of freedom, p-value interpretation, and worked examples.
Understand what p-values really mean, how to calculate them from z-scores and t-scores, significance levels, and the most common misconceptions researchers make.
Learn three methods for detecting outliers: the IQR method, Z-score method, and Modified Z-score. Includes worked examples and guidance on when to remove outliers.
Learn how to calculate the right sample size for surveys, A/B tests, and research studies. Covers the formula, margin of error, confidence level, and finite population correction.
Learn how to perform one-way ANOVA to compare means across multiple groups. Covers the F-statistic, SS/MS calculations, assumptions, and post-hoc tests.
Understand Bayes' theorem with the formula P(A|B) = P(B|A)×P(A)/P(B). Covers prior vs posterior probabilities, tree diagrams, and real-world applications.
Understand the difference between cross products and dot products. Covers formulas, geometric interpretations, the right-hand rule, and physics applications.
Learn the completing the square method step by step. Convert quadratics to vertex form, derive the quadratic formula, and solve equations with worked examples.
Learn synthetic division step by step. Compare with long division, apply the Remainder and Factor Theorems, and find polynomial zeros with worked examples.
Understand confidence intervals correctly. Learn the z and t interval formulas, how to choose confidence levels, the effect of sample size, and common misinterpretations.
Learn how to find the line of best fit using least squares regression. Covers slope and intercept formulas, R-squared, residuals, and assumptions with a full hand-computed example.
Learn implicit differentiation step by step. Understand why we need it, how the chain rule applies, and how to find tangent lines and second derivatives implicitly.
Learn Laplace transforms with a common transforms table, key properties, and step-by-step examples solving first and second order differential equations.
Learn the Poisson distribution for modelling rare events. Covers the PMF formula, mean and variance, cumulative probabilities, and comparison with the binomial distribution.
Learn the density formula ρ = m/V, measurement techniques, common material densities, and applications in buoyancy and material identification with worked examples.
Learn how to calculate percentile ranks, quartiles (Q1, Q2, Q3), IQR, and construct box plots. Covers outlier detection and applications in standardised testing.
Understand kinetic energy (KE = ½mv²) and potential energy (PE = mgh). Covers conservation of energy, elastic potential energy, and the work-energy theorem with worked examples.
Learn Ohm's law (V = IR) with the three formula forms, the Ohm's law triangle, power calculations, and series vs parallel circuit analysis with worked examples.
Learn momentum (p = mv) and impulse (J = FΔt). Covers conservation of momentum, elastic vs inelastic collisions, rocket propulsion, and real-world applications.