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Simplifying 10x(x + 7) = 180 Reorder the terms: 10x(7 + x) = 180 (7 * 10x + x * 10x) = 180 (70x + 10x2) = 180 Solving 70x + 10x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 70x + 10x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 70x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-18 + 7x + x2) = 0 Factor a trinomial. 10((-9 + -1x)(2 + -1x)) = 0 Ignore the factor 10.Subproblem 1
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 = -9Subproblem 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 = {-9, 2}
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