How do you solve a quadratic equation?

A quadratic equation is an equation in the form of ax^2 + bx + c = 0 where x is the variable and a, b, and c are constants. To solve a quadratic equation, there are several methods that can be used, but the most common ones are factoring, completing the square, and using the quadratic formula.

Factoring Method

The factoring method involves finding two numbers that multiply to give the constant term c and add up to give the coefficient of the x-term b. Once these numbers are found, they can be used to rewrite the quadratic equation as (x + p)(x + q) = 0, where p and q are the two numbers. The equation can then be solved by setting each factor equal to zero.

Completing the Square Method

The completing the square method involves manipulating the quadratic equation to make it a perfect square trinomial. This is done by adding and subtracting a constant term that will make the first three terms of the equation a perfect square. The equation can then be solved by taking the square root of both sides and isolating the variable.

Quadratic Formula Method

The quadratic formula is a formula that gives the solutions to any quadratic equation. The formula is x = (-b ± sqrt(b^2 - 4ac)) / 2a, where a, b, and c are the coefficients of the quadratic equation. To use the quadratic formula, simply plug in the values for a, b, and c and simplify.