How do you solve the equation by completing the square: x^2 + 2x - 8 = 0?

1 Answer
Jul 12, 2016

x = 2 and x = -4

Explanation:

Let's rewrite our equation first, before completing the square:

x^2+2x-8=0

x^2+2x + ? = 8 + ?

To complete the square, we take the coefficient on the x-term, namely 2, divide it by 2, and square the result, giving us

(2/2)^(2) = 1^2 = 1

By replacing the ? marks with our number 1, we get

x^2+2x+1 = 9

In this case, we are looking for two numbers whose product gives us 1 and when added together, gives us 2.

Since 1 * 1 = 1 and 1+1 = 2, we can see that the numbers are 1 and 1, which means that we can rewrite our equation in the following way:

(x+1)^(2) = 9

By taking the square root of both sides we get

(x+1) = ± sqrt(9)

x+1 = ± 3

Subtracting 1 from both sides gives us

x = ± 3 -1

So our solutions are x = 2 and x = -4