Need ! : ( follow the process of completing the square to solve 2x2 + 8x - 12 = 0. how will the left side of the equation factor in step 5? a. (2x + 32)2 b. (4x + 8)2 c. (4x + 16)2

Given:
2x² + 8x - 12 = 0

Solution:
The first term 2x² can't be changed to a complete square form. If we want to change it to the complete square form, we need to change 2x² to 4x². So, multiply both sides of the equation by 2
2x² + 8x - 12 = 0
multiplied by 2
4x² + 16x - 24 = 0

then change it to complete quadratic form by adding 16 to both sides
4x² + 16x - 24 = 0
4x² + 16x + 16 - 24 = 16
4x² + 16x + 16 = 16 + 24
4x² + 16x + 16 = 40
(2x + 4)(2x + 4) = 40
(2x + 4)² = 40
This is the complete quadratic form of the equation.

Because there is no option of the solution, we can modify the equation by multiplying the two sides by a square number. I multiply the equation by 4.
(2x + 4)² = 40
4 (2x + 4)² = 4 × 40
4 (2x + 4)² = 160
4 (2x + 4)(2x + 4) = 160
2(2x + 4) 2(2x + 4) = 160
(4x + 8)(4x + 8) = 160
(4x + 8)² = 160

The answer is option b