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Simplifying 2(x + 5)(x + -2) = x(x + 5) + 190 Reorder the terms: 2(5 + x)(x + -2) = x(x + 5) + 190 Reorder the terms: 2(5 + x)(-2 + x) = x(x + 5) + 190 Multiply (5 + x) * (-2 + x) 2(5(-2 + x) + x(-2 + x)) = x(x + 5) + 190 2((-2 * 5 + x * 5) + x(-2 + x)) = x(x + 5) + 190 2((-10 + 5x) + x(-2 + x)) = x(x + 5) + 190 2(-10 + 5x + (-2 * x + x * x)) = x(x + 5) + 190 2(-10 + 5x + (-2x + x2)) = x(x + 5) + 190 Combine like terms: 5x + -2x = 3x 2(-10 + 3x + x2) = x(x + 5) + 190 (-10 * 2 + 3x * 2 + x2 * 2) = x(x + 5) + 190 (-20 + 6x + 2x2) = x(x + 5) + 190 Reorder the terms: -20 + 6x + 2x2 = x(5 + x) + 190 -20 + 6x + 2x2 = (5 * x + x * x) + 190 -20 + 6x + 2x2 = (5x + x2) + 190 Reorder the terms: -20 + 6x + 2x2 = 190 + 5x + x2 Solving -20 + 6x + 2x2 = 190 + 5x + x2 Solving for variable 'x'. Reorder the terms: -20 + -190 + 6x + -5x + 2x2 + -1x2 = 190 + 5x + x2 + -190 + -5x + -1x2 Combine like terms: -20 + -190 = -210 -210 + 6x + -5x + 2x2 + -1x2 = 190 + 5x + x2 + -190 + -5x + -1x2 Combine like terms: 6x + -5x = 1x -210 + 1x + 2x2 + -1x2 = 190 + 5x + x2 + -190 + -5x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -210 + 1x + 1x2 = 190 + 5x + x2 + -190 + -5x + -1x2 Reorder the terms: -210 + 1x + 1x2 = 190 + -190 + 5x + -5x + x2 + -1x2 Combine like terms: 190 + -190 = 0 -210 + 1x + 1x2 = 0 + 5x + -5x + x2 + -1x2 -210 + 1x + 1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 -210 + 1x + 1x2 = 0 + x2 + -1x2 -210 + 1x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -210 + 1x + 1x2 = 0 Factor a trinomial. (-15 + -1x)(14 + -1x) = 0Subproblem 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 '(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 = 14Solution
x = {-15, 14}
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