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Simplifying 32 + 24x + 4x2 = 96 Solving 32 + 24x + 4x2 = 96 Solving for variable 'x'. Reorder the terms: 32 + -96 + 24x + 4x2 = 96 + -96 Combine like terms: 32 + -96 = -64 -64 + 24x + 4x2 = 96 + -96 Combine like terms: 96 + -96 = 0 -64 + 24x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-16 + 6x + x2) = 0 Factor a trinomial. 4((-8 + -1x)(2 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve: Simplifying -8 + -1x = 0 Solving -8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1x = 0 + 8 -1x = 0 + 8 Combine like terms: 0 + 8 = 8 -1x = 8 Divide each side by '-1'. x = -8 Simplifying x = -8Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-8, 2}
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