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Simplifying 2x2 + -5 = 3x2 + -12x + 31 Reorder the terms: -5 + 2x2 = 3x2 + -12x + 31 Reorder the terms: -5 + 2x2 = 31 + -12x + 3x2 Solving -5 + 2x2 = 31 + -12x + 3x2 Solving for variable 'x'. Reorder the terms: -5 + -31 + 12x + 2x2 + -3x2 = 31 + -12x + 3x2 + -31 + 12x + -3x2 Combine like terms: -5 + -31 = -36 -36 + 12x + 2x2 + -3x2 = 31 + -12x + 3x2 + -31 + 12x + -3x2 Combine like terms: 2x2 + -3x2 = -1x2 -36 + 12x + -1x2 = 31 + -12x + 3x2 + -31 + 12x + -3x2 Reorder the terms: -36 + 12x + -1x2 = 31 + -31 + -12x + 12x + 3x2 + -3x2 Combine like terms: 31 + -31 = 0 -36 + 12x + -1x2 = 0 + -12x + 12x + 3x2 + -3x2 -36 + 12x + -1x2 = -12x + 12x + 3x2 + -3x2 Combine like terms: -12x + 12x = 0 -36 + 12x + -1x2 = 0 + 3x2 + -3x2 -36 + 12x + -1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -36 + 12x + -1x2 = 0 Factor a trinomial. (-6 + x)(6 + -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 '(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 = {6, 6}
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