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Simplifying 2x(x + -1) + -7x = 18 + -5(x + 4) Reorder the terms: 2x(-1 + x) + -7x = 18 + -5(x + 4) (-1 * 2x + x * 2x) + -7x = 18 + -5(x + 4) (-2x + 2x2) + -7x = 18 + -5(x + 4) Reorder the terms: -2x + -7x + 2x2 = 18 + -5(x + 4) Combine like terms: -2x + -7x = -9x -9x + 2x2 = 18 + -5(x + 4) Reorder the terms: -9x + 2x2 = 18 + -5(4 + x) -9x + 2x2 = 18 + (4 * -5 + x * -5) -9x + 2x2 = 18 + (-20 + -5x) Combine like terms: 18 + -20 = -2 -9x + 2x2 = -2 + -5x Solving -9x + 2x2 = -2 + -5x Solving for variable 'x'. Reorder the terms: 2 + -9x + 5x + 2x2 = -2 + -5x + 2 + 5x Combine like terms: -9x + 5x = -4x 2 + -4x + 2x2 = -2 + -5x + 2 + 5x Reorder the terms: 2 + -4x + 2x2 = -2 + 2 + -5x + 5x Combine like terms: -2 + 2 = 0 2 + -4x + 2x2 = 0 + -5x + 5x 2 + -4x + 2x2 = -5x + 5x Combine like terms: -5x + 5x = 0 2 + -4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -2x + x2) = 0 Factor a trinomial. 2((1 + -1x)(1 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {1, 1}
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