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