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Simplifying (7x + -7)(x + 5) = 0 Reorder the terms: (-7 + 7x)(x + 5) = 0 Reorder the terms: (-7 + 7x)(5 + x) = 0 Multiply (-7 + 7x) * (5 + x) (-7(5 + x) + 7x * (5 + x)) = 0 ((5 * -7 + x * -7) + 7x * (5 + x)) = 0 ((-35 + -7x) + 7x * (5 + x)) = 0 (-35 + -7x + (5 * 7x + x * 7x)) = 0 (-35 + -7x + (35x + 7x2)) = 0 Combine like terms: -7x + 35x = 28x (-35 + 28x + 7x2) = 0 Solving -35 + 28x + 7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7'. 7(-5 + 4x + x2) = 0 Factor a trinomial. 7((-5 + -1x)(1 + -1x)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 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 = {-5, 1}
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