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Simplifying 12x2 + -48x = 27 Reorder the terms: -48x + 12x2 = 27 Solving -48x + 12x2 = 27 Solving for variable 'x'. Reorder the terms: -27 + -48x + 12x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + -48x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-9 + -16x + 4x2) = 0 Factor a trinomial. 3((-1 + -2x)(9 + -2x)) = 0 Ignore the factor 3.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 '(9 + -2x)' equal to zero and attempt to solve: Simplifying 9 + -2x = 0 Solving 9 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2x = 0 + -9 -2x = 0 + -9 Combine like terms: 0 + -9 = -9 -2x = -9 Divide each side by '-2'. x = 4.5 Simplifying x = 4.5Solution
x = {-0.5, 4.5}
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