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Simplifying (6x2 + -12) + (5x2 + -4x) = 180 Reorder the terms: (-12 + 6x2) + (5x2 + -4x) = 180 Remove parenthesis around (-12 + 6x2) -12 + 6x2 + (5x2 + -4x) = 180 Reorder the terms: -12 + 6x2 + (-4x + 5x2) = 180 Remove parenthesis around (-4x + 5x2) -12 + 6x2 + -4x + 5x2 = 180 Reorder the terms: -12 + -4x + 6x2 + 5x2 = 180 Combine like terms: 6x2 + 5x2 = 11x2 -12 + -4x + 11x2 = 180 Solving -12 + -4x + 11x2 = 180 Solving for variable 'x'. Reorder the terms: -12 + -180 + -4x + 11x2 = 180 + -180 Combine like terms: -12 + -180 = -192 -192 + -4x + 11x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -192 + -4x + 11x2 = 0 Factor a trinomial. (-4 + -1x)(48 + -11x) = 0Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 2
Set the factor '(48 + -11x)' equal to zero and attempt to solve: Simplifying 48 + -11x = 0 Solving 48 + -11x = 0 Move all terms containing x to the left, all other terms to the right. Add '-48' to each side of the equation. 48 + -48 + -11x = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -11x = 0 + -48 -11x = 0 + -48 Combine like terms: 0 + -48 = -48 -11x = -48 Divide each side by '-11'. x = 4.363636364 Simplifying x = 4.363636364Solution
x = {-4, 4.363636364}
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