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Simplifying 5x(x + 8) = 100 Reorder the terms: 5x(8 + x) = 100 (8 * 5x + x * 5x) = 100 (40x + 5x2) = 100 Solving 40x + 5x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 40x + 5x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 40x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-20 + 8x + x2) = 0 Factor a trinomial. 5((-10 + -1x)(2 + -1x)) = 0 Ignore the factor 5.Subproblem 1
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 = -10Subproblem 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 = {-10, 2}
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