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Simplifying (2x2 + -25x) + (3x2 + 60) = 180 Reorder the terms: (-25x + 2x2) + (3x2 + 60) = 180 Remove parenthesis around (-25x + 2x2) -25x + 2x2 + (3x2 + 60) = 180 Reorder the terms: -25x + 2x2 + (60 + 3x2) = 180 Remove parenthesis around (60 + 3x2) -25x + 2x2 + 60 + 3x2 = 180 Reorder the terms: 60 + -25x + 2x2 + 3x2 = 180 Combine like terms: 2x2 + 3x2 = 5x2 60 + -25x + 5x2 = 180 Solving 60 + -25x + 5x2 = 180 Solving for variable 'x'. Reorder the terms: 60 + -180 + -25x + 5x2 = 180 + -180 Combine like terms: 60 + -180 = -120 -120 + -25x + 5x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -120 + -25x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-24 + -5x + x2) = 0 Factor a trinomial. 5((-3 + -1x)(8 + -1x)) = 0 Ignore the factor 5.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 '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {-3, 8}
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