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Simplifying 0 = (x + 9)(9x + 1) Reorder the terms: 0 = (9 + x)(9x + 1) Reorder the terms: 0 = (9 + x)(1 + 9x) Multiply (9 + x) * (1 + 9x) 0 = (9(1 + 9x) + x(1 + 9x)) 0 = ((1 * 9 + 9x * 9) + x(1 + 9x)) 0 = ((9 + 81x) + x(1 + 9x)) 0 = (9 + 81x + (1 * x + 9x * x)) 0 = (9 + 81x + (1x + 9x2)) Combine like terms: 81x + 1x = 82x 0 = (9 + 82x + 9x2) Solving 0 = 9 + 82x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -9 = -9 -9 + -82x + -9x2 = 9 + 82x + 9x2 + -9 + -82x + -9x2 Reorder the terms: -9 + -82x + -9x2 = 9 + -9 + 82x + -82x + 9x2 + -9x2 Combine like terms: 9 + -9 = 0 -9 + -82x + -9x2 = 0 + 82x + -82x + 9x2 + -9x2 -9 + -82x + -9x2 = 82x + -82x + 9x2 + -9x2 Combine like terms: 82x + -82x = 0 -9 + -82x + -9x2 = 0 + 9x2 + -9x2 -9 + -82x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -9 + -82x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 82x + 9x2) = 0 Factor a trinomial. -1((9 + x)(1 + 9x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9Subproblem 2
Set the factor '(1 + 9x)' equal to zero and attempt to solve: Simplifying 1 + 9x = 0 Solving 1 + 9x = 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 + 9x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 9x = 0 + -1 9x = 0 + -1 Combine like terms: 0 + -1 = -1 9x = -1 Divide each side by '9'. x = -0.1111111111 Simplifying x = -0.1111111111Solution
x = {-9, -0.1111111111}
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