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Simplifying 4x + 5 + 2x2 + -12x + 21 = 180 Reorder the terms: 5 + 21 + 4x + -12x + 2x2 = 180 Combine like terms: 5 + 21 = 26 26 + 4x + -12x + 2x2 = 180 Combine like terms: 4x + -12x = -8x 26 + -8x + 2x2 = 180 Solving 26 + -8x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: 26 + -180 + -8x + 2x2 = 180 + -180 Combine like terms: 26 + -180 = -154 -154 + -8x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -154 + -8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-77 + -4x + x2) = 0 Factor a trinomial. 2((-7 + -1x)(11 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. x = -7 Simplifying x = -7Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve: Simplifying 11 + -1x = 0 Solving 11 + -1x = 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 + -1x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1x = 0 + -11 -1x = 0 + -11 Combine like terms: 0 + -11 = -11 -1x = -11 Divide each side by '-1'. x = 11 Simplifying x = 11Solution
x = {-7, 11}
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