Daiana L.

asked • 03/06/19# How do I solve x² + 2x − 8 = 0?

Math math math math math math math math math math

## 2 Answers By Expert Tutors

Eric H. answered • 02/12/21

Math student - love helping other students

When an equation has a squared term in it such as x^{2 }+ 2x - 8 = 0, it's called a *polynomial equation*.

The rule for solving a polynomial equation is to first set it equal to 0, then factor.

Since this equation is already set equal to 0, our first step is to factor the left side.

To factor x^{2} + 2x - 8, we need the factors of -8 that add to +2, which are +4 and -2.

So we have (x + 4)(x - 2) = 0.

Whenever two terms are multiplied together to equal 0,

this means that either one or the other must equal 0.

So if (x + 4)(x - 2) = 0, then either x + 4 = 0 *or* x - 2 = 0.

Solving each equation from here, we subtract 4 from both sides of our first equation

to get x = -4 and we add 2 to both sides of our second equation to get x = 2.

So this equation has two solutions, -4 and 2, and we can put our answer in set notation as {-4, 2}.

Multiply (x+4)(x-2), then you should know the answer!

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Eric W.

(x+4)*(x-2)=0, then X=-4 AND X=2.09/05/19