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Simplifying x2 + 12x + 36 = 2x2 + x + 66 Reorder the terms: 36 + 12x + x2 = 2x2 + x + 66 Reorder the terms: 36 + 12x + x2 = 66 + x + 2x2 Solving 36 + 12x + x2 = 66 + x + 2x2 Solving for variable 'x'. Reorder the terms: 36 + -66 + 12x + -1x + x2 + -2x2 = 66 + x + 2x2 + -66 + -1x + -2x2 Combine like terms: 36 + -66 = -30 -30 + 12x + -1x + x2 + -2x2 = 66 + x + 2x2 + -66 + -1x + -2x2 Combine like terms: 12x + -1x = 11x -30 + 11x + x2 + -2x2 = 66 + x + 2x2 + -66 + -1x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -30 + 11x + -1x2 = 66 + x + 2x2 + -66 + -1x + -2x2 Reorder the terms: -30 + 11x + -1x2 = 66 + -66 + x + -1x + 2x2 + -2x2 Combine like terms: 66 + -66 = 0 -30 + 11x + -1x2 = 0 + x + -1x + 2x2 + -2x2 -30 + 11x + -1x2 = x + -1x + 2x2 + -2x2 Combine like terms: x + -1x = 0 -30 + 11x + -1x2 = 0 + 2x2 + -2x2 -30 + 11x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -30 + 11x + -1x2 = 0 Factor a trinomial. (-6 + x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {6, 5}
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