Question

How can you solve any quadratic equation?

Answer 1

ax 2 + bx + c = 0

when a 0.

There are three basic methods for solving quadratic equations: factoring, using the quadratic formula, and completing the square.

Factoring

To solve a quadratic equation by factoring,

Put all terms on one side of the equal sign, leaving zero on the other side.

Factor.

Set each factor equal to zero.

Solve each of these equations.

Check by inserting your answer in the original equation.

Example 1

Solve x 2 – 6 x = 16.

Following the steps,

x 2 – 6 x = 16 becomes x 2 – 6 x – 16 = 0

Factor.

( x – 8)( x + 2) = 0

Setting each factor to zero, equation

Then to check, equation

Both values, 8 and –2, are solutions to the original equation.

Example 2

Solve y 2 = – 6 y – 5.

Setting all terms equal to zero,

y 2 + 6 y + 5 = 0

Factor.

( y + 5)( y + 1) = 0

Setting each factor to 0, equation

To check, y 2 = –6 y – 5

equation