Question

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?

Answer 1

2x^2+8x-12=0
with form
ax^2+bx+c=0

move c to the other side
2x^2+8x=12

x^2 is multiplied -> divide equation by 2
x^2+4x=6

complete square:
divide b=4 by 2
4*1/2=2

square 2
2^2=4

add 4 to both sides
x^2+4x=6
x^2+4x+4=6+4
x^2+4x+4=10

transform to polynom
(x+2)^2=10

this left side is option B multiplied by a factor of 16 and therefore equal:
(4x + 8)^2
(4*4)x^2+(4*2*8)x+8*8
16x^2+64x+64
x^2+4+4

bonus: calculate root
x+2=+/-sqrt(10)
x=-2+/-sqrt(10)


so it is option B

Answer 2

Complete the square to solve $2x^2 + 8x - 12 = 0$.

Soooooooo, $(4x + 8)^2$ is your answer. :)