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Simplifying 2x2 + 9 = x2 + 10x Reorder the terms: 9 + 2x2 = x2 + 10x Reorder the terms: 9 + 2x2 = 10x + x2 Solving 9 + 2x2 = 10x + x2 Solving for variable 'x'. Reorder the terms: 9 + -10x + 2x2 + -1x2 = 10x + x2 + -10x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 9 + -10x + 1x2 = 10x + x2 + -10x + -1x2 Reorder the terms: 9 + -10x + 1x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 9 + -10x + 1x2 = 0 + x2 + -1x2 9 + -10x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 9 + -10x + 1x2 = 0 Factor a trinomial. (1 + -1x)(9 + -1x) = 0Subproblem 1
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 = 1Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 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 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {1, 9}
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