Question

Solve x2 - 8x = 20 by completing the square. Which is the solution set of the equation?

{-22,14}
{-14,22}
{-10,2}
{-2,10}

Answer 1

{-2,10}

Explanation:

x^2 - 8x = 20

Take the coefficient of x

-8

Divide by 2

-8/2 =-4

Square it

(-4)^2 =16

Add this to each side

x^2 - 8x+16 = 20+16

x^2 - 8x+16 = 36

The left hand side becomes( x + (-8/2) )^2

(x - 4)^2 = 36

Take the square root of each side

sqrt((x - 4)^2) =±sqrt( 36)

x-4 = ±6

Add 4 to each side

x-4+4 = 4±6

x = 4±6

x = 4+6 x = 4-6

x = 10 x = -2