Solving Quadratic Equations

The quadratic formula is used to solve quadratic equations when other methods are more difficult. To use the quadratic formula to solve a quadratic equation, begin by rewriting the equation in standard form
and c are coefficients. Once you have identified the values of the coefficients, substitute those values into the quadratic formul ax² + bx + c = 0, where a ≠ 0 & discriminant.

If the discriminant is zero, there is only one root: zero. If the discriminant is positive, there are two different real roots. If the discriminant is negative, there are no real roots.

To solve a quadratic equation by factoring, begin by rewriting the equation in standard form, if necessary.

Factor the side with the variable then set each of the factors equal to zero and solve the resulting linear equations.

Check your answers by substituting the roots you found into the original equation. If, when writing the equation in standard form, you have an equation in the form
 or
, set
 or
 and take the square root of c. If c = 0, the only real root is zero.

If c is positive, there are two real roots—the positive and negative square root values.

If c is negative, there are no real roots because you cannot take the square root of a negative number.

To solve a quadratic equation by completing the square, rewrite the equation so that all terms containing the variable are on the left side of the equal sign, and all the constants are on the right side of the equal sign.

Make sure the coefficient of the squared term is 1. If there is a coefficient with the squared term, divide each term on both sides of the equal side by that number.

Next, work with the coefficient of the single-variable term. Square half of this coefficient, and add that value to both sides. Now you can factor the left side (the side containing the variable) as the square of a binomial.