Question

Which Of the following is the real result of the equation below after completing the square and factoring?
x^2 - 4x + 2 = 10

A.) (x-2)^2 = 12

B.) (x-2)^2 = 14

C.) (x+2)^2 = 14

D.) (x+2)^2 = 8

Answer 1

x² - 4x + 2 = 10

Separate variables and constants aside by subtracting 2 from each side.

x² - 4x + 2 -2= 10 -2

x² - 4x= 8

To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

x² - 4x + 2²= 8 + 2²

x² - 4x + 4 = 8 + 4

(x - 2) ² = 12

So option A is correct.