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Simplifying x(x + 5) * 12 = 1800 Reorder the terms: x(5 + x) * 12 = 1800 Reorder the terms for easier multiplication: 12x(5 + x) = 1800 (5 * 12x + x * 12x) = 1800 (60x + 12x2) = 1800 Solving 60x + 12x2 = 1800 Solving for variable 'x'. Reorder the terms: -1800 + 60x + 12x2 = 1800 + -1800 Combine like terms: 1800 + -1800 = 0 -1800 + 60x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(-150 + 5x + x2) = 0 Factor a trinomial. 12((-15 + -1x)(10 + -1x)) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve: Simplifying -15 + -1x = 0 Solving -15 + -1x = 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 + -1x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1x = 0 + 15 -1x = 0 + 15 Combine like terms: 0 + 15 = 15 -1x = 15 Divide each side by '-1'. x = -15 Simplifying x = -15Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {-15, 10}
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