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Simplifying 3x + 6 = x2 + -8x + 16 Reorder the terms: 6 + 3x = x2 + -8x + 16 Reorder the terms: 6 + 3x = 16 + -8x + x2 Solving 6 + 3x = 16 + -8x + x2 Solving for variable 'x'. Reorder the terms: 6 + -16 + 3x + 8x + -1x2 = 16 + -8x + x2 + -16 + 8x + -1x2 Combine like terms: 6 + -16 = -10 -10 + 3x + 8x + -1x2 = 16 + -8x + x2 + -16 + 8x + -1x2 Combine like terms: 3x + 8x = 11x -10 + 11x + -1x2 = 16 + -8x + x2 + -16 + 8x + -1x2 Reorder the terms: -10 + 11x + -1x2 = 16 + -16 + -8x + 8x + x2 + -1x2 Combine like terms: 16 + -16 = 0 -10 + 11x + -1x2 = 0 + -8x + 8x + x2 + -1x2 -10 + 11x + -1x2 = -8x + 8x + x2 + -1x2 Combine like terms: -8x + 8x = 0 -10 + 11x + -1x2 = 0 + x2 + -1x2 -10 + 11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -10 + 11x + -1x2 = 0 Factor a trinomial. (-10 + x)(1 + -1x) = 0Subproblem 1
Set the factor '(-10 + x)' equal to zero and attempt to solve: Simplifying -10 + x = 0 Solving -10 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + x = 0 + 10 x = 0 + 10 Combine like terms: 0 + 10 = 10 x = 10 Simplifying x = 10Subproblem 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 = {10, 1}
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