Question

What are the two solutions of the equation x^2 − 10 = 90 ?
Show work :)

Answer 1

x = 5 ±√115

Explanation:

x² - 10x - 90 = 0

You can solve for x by doing it in 2 ways: Completing the square and by using the quadratic formula

Completing the Square

(x² - 10x + 25) - 25 - 90 = 0

(x - 5)² - 115 = 0

(x - 5)² = 115

x - 5 = ±√115

x = 5 ±√115

Quadratic Formula

√460 = √4 X √115

Hence 2√115

Answer 2

-10 and 10

Explanation:

subtracting what is to the right of the equal sign from both sides of the equation : x^2-10-(90)=0

step 1 - A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

(at the end of step 1 it should look like this) = (x + 10) • (x - 10)

solve as many equations as there are terms in the product

any solution of term = 0 solves product = 0 as well.