Find the values of x for which f (x) = g (x). (Enter your answers as a comma-separated list.) f (x) = x2, g (x) = x + 20

Given

function f (x) = x²

function g (x) = x + 20

Solution:

Substitute f (x) with x² and substitute g (x) with (x + 20)

f (x) = g (x)

x² = x + 20

Move all terms to the left side. After moving, the positive ones become negative.

x² = x + 20

x² - x - 20 = 0

I break - x into - 5x + 4x

x² - x - 20 = 0

x² - 5x + 4x - 20 = 0

Factorize x² - 5x

x² - 5x + 4x - 20 = 0

x (x - 5) + 4x - 20 = 0

Now factorize 4x - 20

x (x - 5) + 4x - 20 = 0

x (x - 5) + 4 (x - 5) = 0

Separate (x - 5) from all terms using distributive property, the remaining one is (x + 4)

x (x - 5) + 4 (x - 5) = 0

(x - 5) (x + 4) = 0

The solution

x - 5 = 0

x = 5

or

x + 4 = 0

x = - 4

f (x) and g (x) will be both equal if the value of x is either 5 or - 4

f (x) = x2 + 2x + 1, g (x) = 11x - 19 x 2 + 2x + 1 = 11x - 19 x2 - 9x + 20 = 0 (x-4) (x-5) = 0 x = 4, 5