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
