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Simplifying 9x + 5 = x2 + 13 Reorder the terms: 5 + 9x = x2 + 13 Reorder the terms: 5 + 9x = 13 + x2 Solving 5 + 9x = 13 + x2 Solving for variable 'x'. Reorder the terms: 5 + -13 + 9x + -1x2 = 13 + x2 + -13 + -1x2 Combine like terms: 5 + -13 = -8 -8 + 9x + -1x2 = 13 + x2 + -13 + -1x2 Reorder the terms: -8 + 9x + -1x2 = 13 + -13 + x2 + -1x2 Combine like terms: 13 + -13 = 0 -8 + 9x + -1x2 = 0 + x2 + -1x2 -8 + 9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -8 + 9x + -1x2 = 0 Factor a trinomial. (-8 + x)(1 + -1x) = 0Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Simplifying x = 8Subproblem 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 = {8, 1}
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