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Simplifying 11565 = x2 + -15x + 65 Reorder the terms: 11565 = 65 + -15x + x2 Solving 11565 = 65 + -15x + x2 Solving for variable 'x'. Combine like terms: 11565 + -65 = 11500 11500 + 15x + -1x2 = 65 + -15x + x2 + -65 + 15x + -1x2 Reorder the terms: 11500 + 15x + -1x2 = 65 + -65 + -15x + 15x + x2 + -1x2 Combine like terms: 65 + -65 = 0 11500 + 15x + -1x2 = 0 + -15x + 15x + x2 + -1x2 11500 + 15x + -1x2 = -15x + 15x + x2 + -1x2 Combine like terms: -15x + 15x = 0 11500 + 15x + -1x2 = 0 + x2 + -1x2 11500 + 15x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 11500 + 15x + -1x2 = 0 Factor a trinomial. (115 + -1x)(100 + x) = 0Subproblem 1
Set the factor '(115 + -1x)' equal to zero and attempt to solve: Simplifying 115 + -1x = 0 Solving 115 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-115' to each side of the equation. 115 + -115 + -1x = 0 + -115 Combine like terms: 115 + -115 = 0 0 + -1x = 0 + -115 -1x = 0 + -115 Combine like terms: 0 + -115 = -115 -1x = -115 Divide each side by '-1'. x = 115 Simplifying x = 115Subproblem 2
Set the factor '(100 + x)' equal to zero and attempt to solve: Simplifying 100 + x = 0 Solving 100 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + x = 0 + -100 Combine like terms: 100 + -100 = 0 0 + x = 0 + -100 x = 0 + -100 Combine like terms: 0 + -100 = -100 x = -100 Simplifying x = -100Solution
x = {115, -100}
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