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Simplifying 9x2 + -12x + 4 = x2 + 8x + 16 Reorder the terms: 4 + -12x + 9x2 = x2 + 8x + 16 Reorder the terms: 4 + -12x + 9x2 = 16 + 8x + x2 Solving 4 + -12x + 9x2 = 16 + 8x + x2 Solving for variable 'x'. Reorder the terms: 4 + -16 + -12x + -8x + 9x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Combine like terms: 4 + -16 = -12 -12 + -12x + -8x + 9x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Combine like terms: -12x + -8x = -20x -12 + -20x + 9x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Combine like terms: 9x2 + -1x2 = 8x2 -12 + -20x + 8x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Reorder the terms: -12 + -20x + 8x2 = 16 + -16 + 8x + -8x + x2 + -1x2 Combine like terms: 16 + -16 = 0 -12 + -20x + 8x2 = 0 + 8x + -8x + x2 + -1x2 -12 + -20x + 8x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 -12 + -20x + 8x2 = 0 + x2 + -1x2 -12 + -20x + 8x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -12 + -20x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-3 + -5x + 2x2) = 0 Factor a trinomial. 4((-1 + -2x)(3 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-0.5, 3}
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