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Simplifying 78 = 3x2 + -60x + 375 Reorder the terms: 78 = 375 + -60x + 3x2 Solving 78 = 375 + -60x + 3x2 Solving for variable 'x'. Combine like terms: 78 + -375 = -297 -297 + 60x + -3x2 = 375 + -60x + 3x2 + -375 + 60x + -3x2 Reorder the terms: -297 + 60x + -3x2 = 375 + -375 + -60x + 60x + 3x2 + -3x2 Combine like terms: 375 + -375 = 0 -297 + 60x + -3x2 = 0 + -60x + 60x + 3x2 + -3x2 -297 + 60x + -3x2 = -60x + 60x + 3x2 + -3x2 Combine like terms: -60x + 60x = 0 -297 + 60x + -3x2 = 0 + 3x2 + -3x2 -297 + 60x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -297 + 60x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-99 + 20x + -1x2) = 0 Factor a trinomial. 3((-11 + x)(9 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-11 + x)' equal to zero and attempt to solve: Simplifying -11 + x = 0 Solving -11 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + x = 0 + 11 x = 0 + 11 Combine like terms: 0 + 11 = 11 x = 11 Simplifying x = 11Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 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 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {11, 9}
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