Solve linear and polynomial equations with step-by-step solutions and graphical visualization.
Math Equation Solver finds variable values that make a linear or polynomial equation true. It presents the algebraic result with intermediate transformations and a graph that helps connect each real solution to the equation's shape. The most common mistake is treating the graph as the final numerical answer. Its scale can hide a root or make an intercept look slightly displaced, so use the stated solutions and substitution checks for exact conclusions.
A concrete input and expected output from the current implementation.
Input
x^2 - 5*x + 6 = 0
Expected output
Solutions: x = 2 and x = 3 x^2 - 5*x + 6 = 0 (x - 2)*(x - 3) = 0 x - 2 = 0 or x - 3 = 0 x = 2 or x = 3
The polynomial factors as (x - 2)(x - 3). A product equals zero when at least one factor equals zero; substitution confirms that both 2 and 3 make the original expression equal zero.
For a linear equation, the solver simplifies both sides and isolates the variable using operations that preserve equality. For a polynomial equation, it first treats the problem as finding the zeros of a polynomial. The displayed steps may expose factors, reduce simpler factors to zero, and list each resulting value that satisfies the original equation.
The visualization gives a geometric view of the equation. For P(x) = 0, each real solution corresponds to an x-coordinate where the polynomial's graph meets the x-axis. A crossing is not required: an even-multiplicity root can touch the axis and turn back. Nonreal roots cannot appear as ordinary x-axis intercepts.
No. A graph is useful for checking the locations and behavior of real roots, but its viewing range and resolution can conceal features. Nonreal roots also have no ordinary x-axis intercept. Use the algebraic solution as the result, and verify listed values by substituting them into the original equation.
That behavior can indicate a root with even multiplicity. For example, (x - 2)^2 = 0 has the solution x = 2, but the squared factor keeps the polynomial nonnegative near that point. The graph reaches zero at x = 2 and turns back instead of changing sign.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
Calculate percentages, percentage change, and what percent one number is of another with step-by-step breakdowns.
Calculate tips and split bills between multiple people with customizable tip percentages and rounding options.
Calculate monthly payments, total interest, and generate amortization schedules for loans and mortgages.
Calculate Body Mass Index from height and weight with category classification and healthy range guidance.
Calculate sale prices, savings amounts, and final costs after single or stacked percentage discounts.
Compute mean, median, mode, standard deviation, variance, and other descriptive statistics from a data set.