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Simplifying (5x + 2)(x + -1) = 7(x + -1) Reorder the terms: (2 + 5x)(x + -1) = 7(x + -1) Reorder the terms: (2 + 5x)(-1 + x) = 7(x + -1) Multiply (2 + 5x) * (-1 + x) (2(-1 + x) + 5x * (-1 + x)) = 7(x + -1) ((-1 * 2 + x * 2) + 5x * (-1 + x)) = 7(x + -1) ((-2 + 2x) + 5x * (-1 + x)) = 7(x + -1) (-2 + 2x + (-1 * 5x + x * 5x)) = 7(x + -1) (-2 + 2x + (-5x + 5x2)) = 7(x + -1) Combine like terms: 2x + -5x = -3x (-2 + -3x + 5x2) = 7(x + -1) Reorder the terms: -2 + -3x + 5x2 = 7(-1 + x) -2 + -3x + 5x2 = (-1 * 7 + x * 7) -2 + -3x + 5x2 = (-7 + 7x) Solving -2 + -3x + 5x2 = -7 + 7x Solving for variable 'x'. Reorder the terms: -2 + 7 + -3x + -7x + 5x2 = -7 + 7x + 7 + -7x Combine like terms: -2 + 7 = 5 5 + -3x + -7x + 5x2 = -7 + 7x + 7 + -7x Combine like terms: -3x + -7x = -10x 5 + -10x + 5x2 = -7 + 7x + 7 + -7x Reorder the terms: 5 + -10x + 5x2 = -7 + 7 + 7x + -7x Combine like terms: -7 + 7 = 0 5 + -10x + 5x2 = 0 + 7x + -7x 5 + -10x + 5x2 = 7x + -7x Combine like terms: 7x + -7x = 0 5 + -10x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + -2x + x2) = 0 Factor a trinomial. 5((1 + -1x)(1 + -1x)) = 0 Ignore the factor 5.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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