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Simplifying 7(x + -3) + -5(x2 + -1) = x2 + -5(x + 2) Reorder the terms: 7(-3 + x) + -5(x2 + -1) = x2 + -5(x + 2) (-3 * 7 + x * 7) + -5(x2 + -1) = x2 + -5(x + 2) (-21 + 7x) + -5(x2 + -1) = x2 + -5(x + 2) Reorder the terms: -21 + 7x + -5(-1 + x2) = x2 + -5(x + 2) -21 + 7x + (-1 * -5 + x2 * -5) = x2 + -5(x + 2) -21 + 7x + (5 + -5x2) = x2 + -5(x + 2) Reorder the terms: -21 + 5 + 7x + -5x2 = x2 + -5(x + 2) Combine like terms: -21 + 5 = -16 -16 + 7x + -5x2 = x2 + -5(x + 2) Reorder the terms: -16 + 7x + -5x2 = x2 + -5(2 + x) -16 + 7x + -5x2 = x2 + (2 * -5 + x * -5) -16 + 7x + -5x2 = x2 + (-10 + -5x) Reorder the terms: -16 + 7x + -5x2 = -10 + -5x + x2 Solving -16 + 7x + -5x2 = -10 + -5x + x2 Solving for variable 'x'. Reorder the terms: -16 + 10 + 7x + 5x + -5x2 + -1x2 = -10 + -5x + x2 + 10 + 5x + -1x2 Combine like terms: -16 + 10 = -6 -6 + 7x + 5x + -5x2 + -1x2 = -10 + -5x + x2 + 10 + 5x + -1x2 Combine like terms: 7x + 5x = 12x -6 + 12x + -5x2 + -1x2 = -10 + -5x + x2 + 10 + 5x + -1x2 Combine like terms: -5x2 + -1x2 = -6x2 -6 + 12x + -6x2 = -10 + -5x + x2 + 10 + 5x + -1x2 Reorder the terms: -6 + 12x + -6x2 = -10 + 10 + -5x + 5x + x2 + -1x2 Combine like terms: -10 + 10 = 0 -6 + 12x + -6x2 = 0 + -5x + 5x + x2 + -1x2 -6 + 12x + -6x2 = -5x + 5x + x2 + -1x2 Combine like terms: -5x + 5x = 0 -6 + 12x + -6x2 = 0 + x2 + -1x2 -6 + 12x + -6x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -6 + 12x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-1 + 2x + -1x2) = 0 Factor a trinomial. 6((-1 + x)(1 + -1x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 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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