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Simplifying 9 = 8x2 + 9x + 10 Reorder the terms: 9 = 10 + 9x + 8x2 Solving 9 = 10 + 9x + 8x2 Solving for variable 'x'. Combine like terms: 9 + -10 = -1 -1 + -9x + -8x2 = 10 + 9x + 8x2 + -10 + -9x + -8x2 Reorder the terms: -1 + -9x + -8x2 = 10 + -10 + 9x + -9x + 8x2 + -8x2 Combine like terms: 10 + -10 = 0 -1 + -9x + -8x2 = 0 + 9x + -9x + 8x2 + -8x2 -1 + -9x + -8x2 = 9x + -9x + 8x2 + -8x2 Combine like terms: 9x + -9x = 0 -1 + -9x + -8x2 = 0 + 8x2 + -8x2 -1 + -9x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -1 + -9x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 9x + 8x2) = 0 Factor a trinomial. -1((1 + x)(1 + 8x)) = 0 Ignore the factor -1.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 + 8x)' equal to zero and attempt to solve: Simplifying 1 + 8x = 0 Solving 1 + 8x = 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 + 8x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8x = 0 + -1 8x = 0 + -1 Combine like terms: 0 + -1 = -1 8x = -1 Divide each side by '8'. x = -0.125 Simplifying x = -0.125Solution
x = {-1, -0.125}
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