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Simplifying 10x2 + 20x + 30 = 180 Reorder the terms: 30 + 20x + 10x2 = 180 Solving 30 + 20x + 10x2 = 180 Solving for variable 'x'. Reorder the terms: 30 + -180 + 20x + 10x2 = 180 + -180 Combine like terms: 30 + -180 = -150 -150 + 20x + 10x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -150 + 20x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-15 + 2x + x2) = 0 Factor a trinomial. 10((-5 + -1x)(3 + -1x)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
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 = 3Solution
x = {-5, 3}
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