Question

Quadratic equations: Factoring

Answer 1

2x2 +12x=32
2x2+12x-32=0 ( 2*32=64, 16*4=64.)
2x2 + 16x-4x-32=0
2x2-4x+16x-32=0
2x(x-2) +16(x-2)=0
(2x+16)(x-2)=0
x=-16/2 or x=2
{x=-8,2}

Answer 2

2(x - 2)(x + 8)

x = 2, x = -8

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))

• 2(x - 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