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Simplifying (5 + -1x)(9 + x) = 49 Multiply (5 + -1x) * (9 + x) (5(9 + x) + -1x * (9 + x)) = 49 ((9 * 5 + x * 5) + -1x * (9 + x)) = 49 ((45 + 5x) + -1x * (9 + x)) = 49 (45 + 5x + (9 * -1x + x * -1x)) = 49 (45 + 5x + (-9x + -1x2)) = 49 Combine like terms: 5x + -9x = -4x (45 + -4x + -1x2) = 49 Solving 45 + -4x + -1x2 = 49 Solving for variable 'x'. Reorder the terms: 45 + -49 + -4x + -1x2 = 49 + -49 Combine like terms: 45 + -49 = -4 -4 + -4x + -1x2 = 49 + -49 Combine like terms: 49 + -49 = 0 -4 + -4x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 4x + x2) = 0 Factor a trinomial. -1((2 + x)(2 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-2, -2}
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