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Simplifying 4x2 + 82x + -180 = 0 Reorder the terms: -180 + 82x + 4x2 = 0 Solving -180 + 82x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-90 + 41x + 2x2) = 0 Factor a trinomial. 2((-45 + -2x)(2 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-45 + -2x)' equal to zero and attempt to solve: Simplifying -45 + -2x = 0 Solving -45 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + -2x = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -2x = 0 + 45 -2x = 0 + 45 Combine like terms: 0 + 45 = 45 -2x = 45 Divide each side by '-2'. x = -22.5 Simplifying x = -22.5Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-22.5, 2}
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