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Simplifying 16x2 + 24x + 9 = 81 Reorder the terms: 9 + 24x + 16x2 = 81 Solving 9 + 24x + 16x2 = 81 Solving for variable 'x'. Reorder the terms: 9 + -81 + 24x + 16x2 = 81 + -81 Combine like terms: 9 + -81 = -72 -72 + 24x + 16x2 = 81 + -81 Combine like terms: 81 + -81 = 0 -72 + 24x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-9 + 3x + 2x2) = 0 Factor a trinomial. 8((-3 + -1x)(3 + -2x)) = 0 Ignore the factor 8.Subproblem 1
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 = -3Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {-3, 1.5}
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