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Simplifying 100 + -24x = 2x2 + 10 Reorder the terms: 100 + -24x = 10 + 2x2 Solving 100 + -24x = 10 + 2x2 Solving for variable 'x'. Reorder the terms: 100 + -10 + -24x + -2x2 = 10 + 2x2 + -10 + -2x2 Combine like terms: 100 + -10 = 90 90 + -24x + -2x2 = 10 + 2x2 + -10 + -2x2 Reorder the terms: 90 + -24x + -2x2 = 10 + -10 + 2x2 + -2x2 Combine like terms: 10 + -10 = 0 90 + -24x + -2x2 = 0 + 2x2 + -2x2 90 + -24x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 90 + -24x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(45 + -12x + -1x2) = 0 Factor a trinomial. 2((3 + -1x)(15 + x)) = 0 Ignore the factor 2.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 '(15 + x)' equal to zero and attempt to solve: Simplifying 15 + x = 0 Solving 15 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + x = 0 + -15 x = 0 + -15 Combine like terms: 0 + -15 = -15 x = -15 Simplifying x = -15Solution
x = {3, -15}
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