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Simplifying x2 + 10x + x2 + -2x = 3x2 + 12 Reorder the terms: 10x + -2x + x2 + x2 = 3x2 + 12 Combine like terms: 10x + -2x = 8x 8x + x2 + x2 = 3x2 + 12 Combine like terms: x2 + x2 = 2x2 8x + 2x2 = 3x2 + 12 Reorder the terms: 8x + 2x2 = 12 + 3x2 Solving 8x + 2x2 = 12 + 3x2 Solving for variable 'x'. Reorder the terms: -12 + 8x + 2x2 + -3x2 = 12 + 3x2 + -12 + -3x2 Combine like terms: 2x2 + -3x2 = -1x2 -12 + 8x + -1x2 = 12 + 3x2 + -12 + -3x2 Reorder the terms: -12 + 8x + -1x2 = 12 + -12 + 3x2 + -3x2 Combine like terms: 12 + -12 = 0 -12 + 8x + -1x2 = 0 + 3x2 + -3x2 -12 + 8x + -1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -12 + 8x + -1x2 = 0 Factor a trinomial. (-6 + x)(2 + -1x) = 0Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {6, 2}
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