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Simplifying 8545 = x2 + 15x + 45 Reorder the terms: 8545 = 45 + 15x + x2 Solving 8545 = 45 + 15x + x2 Solving for variable 'x'. Combine like terms: 8545 + -45 = 8500 8500 + -15x + -1x2 = 45 + 15x + x2 + -45 + -15x + -1x2 Reorder the terms: 8500 + -15x + -1x2 = 45 + -45 + 15x + -15x + x2 + -1x2 Combine like terms: 45 + -45 = 0 8500 + -15x + -1x2 = 0 + 15x + -15x + x2 + -1x2 8500 + -15x + -1x2 = 15x + -15x + x2 + -1x2 Combine like terms: 15x + -15x = 0 8500 + -15x + -1x2 = 0 + x2 + -1x2 8500 + -15x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 8500 + -15x + -1x2 = 0 Factor a trinomial. (85 + -1x)(100 + x) = 0Subproblem 1
Set the factor '(85 + -1x)' equal to zero and attempt to solve: Simplifying 85 + -1x = 0 Solving 85 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-85' to each side of the equation. 85 + -85 + -1x = 0 + -85 Combine like terms: 85 + -85 = 0 0 + -1x = 0 + -85 -1x = 0 + -85 Combine like terms: 0 + -85 = -85 -1x = -85 Divide each side by '-1'. x = 85 Simplifying x = 85Subproblem 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 = {85, -100}
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