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Simplifying 8(1 + -1x)(x + 7) = 0 Reorder the terms: 8(1 + -1x)(7 + x) = 0 Multiply (1 + -1x) * (7 + x) 8(1(7 + x) + -1x * (7 + x)) = 0 8((7 * 1 + x * 1) + -1x * (7 + x)) = 0 8((7 + 1x) + -1x * (7 + x)) = 0 8(7 + 1x + (7 * -1x + x * -1x)) = 0 8(7 + 1x + (-7x + -1x2)) = 0 Combine like terms: 1x + -7x = -6x 8(7 + -6x + -1x2) = 0 (7 * 8 + -6x * 8 + -1x2 * 8) = 0 (56 + -48x + -8x2) = 0 Solving 56 + -48x + -8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(7 + -6x + -1x2) = 0 Factor a trinomial. 8((1 + -1x)(7 + x)) = 0 Ignore the factor 8.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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Solution
x = {1, -7}
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