# How do you solve quadratic equation: x^2+2x-8 by factoring?

Aug 22, 2016

$x = 2 \mathmr{and} x = - 4$

#### Explanation:

There is a contradiction in the question.

It is an expression, not an equation, so it cannot be solved.
However, let's assume it was supposed to read as

${x}^{2} + 2 x - 8 = 0 \text{ make a quadratic equation equal to 0}$

Find the factors.
Reading from the back we have the following information.

"Find the factors of 8 which subtract (-) to make 2".
"The signs will be different (because of -)"
"There must be more positives. (because of +2)"

Factors of 8 are either 8 x 1 or 4 x 2 .

4-2 = 2 , so these are the factors we want.

Write the factors in the brackets: $\left(x \text{ "4)(x" } 2\right) = 0$

Fill in the signs: $\left(x + 4\right) \left(x - 2\right) = 0 \text{ "4>2, 4 " is positive}$

Now because the answer is 0, each bracket could be 0.

If $x + 4 = 0 \text{ } \Rightarrow x = - 4$

If $x - 2 = 0 \text{ } \Rightarrow x = 2$

These are the solutions to the equation.