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Simplifying 3x + 8 = x2 + 10 Reorder the terms: 8 + 3x = x2 + 10 Reorder the terms: 8 + 3x = 10 + x2 Solving 8 + 3x = 10 + x2 Solving for variable 'x'. Reorder the terms: 8 + -10 + 3x + -1x2 = 10 + x2 + -10 + -1x2 Combine like terms: 8 + -10 = -2 -2 + 3x + -1x2 = 10 + x2 + -10 + -1x2 Reorder the terms: -2 + 3x + -1x2 = 10 + -10 + x2 + -1x2 Combine like terms: 10 + -10 = 0 -2 + 3x + -1x2 = 0 + x2 + -1x2 -2 + 3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -2 + 3x + -1x2 = 0 Factor a trinomial. (-2 + x)(1 + -1x) = 0Subproblem 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 '(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 = {2, 1}
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