Question

Which statement describes the first step to solve the equation by completing the square?
2x²+12x=32



Add 6 to each side of the equation.

Multiply both sides of the equation by 1/6 .

Multiply both sides of the equation by 1/2 .

Add 36 to each side of the equation.

Answer 1

None of the statements are true,

Proof:
Solve for x over the real numbers:
2 x^2 + 12 x = 32

Subtract 32 from both sides:
2 x^2 + 12 x - 32 = 0

2 x^2 + 12 x - 32 = 2 (x^2 + 6 x - 16):
2 (x^2 + 6 x - 16) = 0

Divide both sides by 2:
x^2 + 6 x - 16 = 0

x = (-6 ± sqrt(6^2 - 4 (-16)))/2 = (-6 ± sqrt(36 + 64))/2 = (-6 ± sqrt(100))/2:
x = (-6 + sqrt(100))/2 or x = (-6 - sqrt(100))/2

sqrt(100) = sqrt(4×25) = sqrt(2^2×5^2) = 2×5 = 10:
x = (-6 + 10)/2 or x = (-6 - 10)/2

(-6 + 10)/2 = 4/2 = 2:
x = 2 or x = (-6 - 10)/2

(-6 - 10)/2 = -16/2 = -8:

Answer:  x = 2 or x = -8