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Simplifying 100 = 2(x + 11)(x + -5) + -1x(x + 11) Reorder the terms: 100 = 2(11 + x)(x + -5) + -1x(x + 11) Reorder the terms: 100 = 2(11 + x)(-5 + x) + -1x(x + 11) Multiply (11 + x) * (-5 + x) 100 = 2(11(-5 + x) + x(-5 + x)) + -1x(x + 11) 100 = 2((-5 * 11 + x * 11) + x(-5 + x)) + -1x(x + 11) 100 = 2((-55 + 11x) + x(-5 + x)) + -1x(x + 11) 100 = 2(-55 + 11x + (-5 * x + x * x)) + -1x(x + 11) 100 = 2(-55 + 11x + (-5x + x2)) + -1x(x + 11) Combine like terms: 11x + -5x = 6x 100 = 2(-55 + 6x + x2) + -1x(x + 11) 100 = (-55 * 2 + 6x * 2 + x2 * 2) + -1x(x + 11) 100 = (-110 + 12x + 2x2) + -1x(x + 11) Reorder the terms: 100 = -110 + 12x + 2x2 + -1x(11 + x) 100 = -110 + 12x + 2x2 + (11 * -1x + x * -1x) 100 = -110 + 12x + 2x2 + (-11x + -1x2) Reorder the terms: 100 = -110 + 12x + -11x + 2x2 + -1x2 Combine like terms: 12x + -11x = 1x 100 = -110 + 1x + 2x2 + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 100 = -110 + 1x + 1x2 Solving 100 = -110 + 1x + 1x2 Solving for variable 'x'. Combine like terms: 100 + 110 = 210 210 + -1x + -1x2 = -110 + 1x + 1x2 + 110 + -1x + -1x2 Reorder the terms: 210 + -1x + -1x2 = -110 + 110 + 1x + -1x + 1x2 + -1x2 Combine like terms: -110 + 110 = 0 210 + -1x + -1x2 = 0 + 1x + -1x + 1x2 + -1x2 210 + -1x + -1x2 = 1x + -1x + 1x2 + -1x2 Combine like terms: 1x + -1x = 0 210 + -1x + -1x2 = 0 + 1x2 + -1x2 210 + -1x + -1x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 210 + -1x + -1x2 = 0 Factor a trinomial. (14 + -1x)(15 + x) = 0Subproblem 1
Set the factor '(14 + -1x)' equal to zero and attempt to solve: Simplifying 14 + -1x = 0 Solving 14 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1x = 0 + -14 -1x = 0 + -14 Combine like terms: 0 + -14 = -14 -1x = -14 Divide each side by '-1'. x = 14 Simplifying x = 14Subproblem 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 = {14, -15}
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