Answer:
2(x - 2)(x + 8)
x = 2, x = -8
Step-by-step explanation:
Hello!
Set the given equation to standard form \(ax^2 + bx + c = 0\):
- 2x² + 12x = 32
- 2x² + 12x - 32 = 0
Factor out 2:
- 2x² + 12x - 32 = 0
- 2(x² + 6x - 16)
Find two terms that multiply to "c" (-16) and add up to "b" (6x)
Two terms that work are 8 and -2
Expand the expression:
- 2(x² + 6x - 16)
- 2(x² + 8x - 2x - 16)
Factor by grouping:
- 2(x² + 8x - 2x - 16)
- 2(x(x + 8) - 2(x + 8))
The factored expression is 2(x - 2)(x + 8).
Use the zero product property to solve for x:
- 2(x - 2)(x + 8) = 0
- x - 2 = 0, x + 8 = 0
- x = 2, x= -8
x can be 2 or -8
