Question

Given: 2x^2+ 32x + 16 = 0

Step 1: x^2+ 16x +8=0
Step x^2+ 16x = -8
Write numbers in each box to correctly complete the square In Step 3.
Step 3: x^2+ 16x +

Answer 1

Step 3: x² + 6x + 64 = -8 + 64

Explanation:

At step 3 add 64 on both sides to complete the square.

so x² + 6x = -8

becomes x² + 6x + 64 = -8 + 64 when 64 is added both sides giving us step 3.

continuing from there, we get

x² + 6x + 64 = 56

we then use a² + 2ab + b² = (a + b)² on the left side to get

(x + 8)² = 56 (solve the equation for x)

by taking the root on both sides

√(x + 8)² = √56

x + 8 = +- 2√14 (separate the equations

x + 8 = 2√14

x + 8 = -2√14

Solving for x

x = 2√14 - 8 or x = -2√14 - 8