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Simplifying 10x2 + -5x + 11 = 9x2 + x + 83 Reorder the terms: 11 + -5x + 10x2 = 9x2 + x + 83 Reorder the terms: 11 + -5x + 10x2 = 83 + x + 9x2 Solving 11 + -5x + 10x2 = 83 + x + 9x2 Solving for variable 'x'. Reorder the terms: 11 + -83 + -5x + -1x + 10x2 + -9x2 = 83 + x + 9x2 + -83 + -1x + -9x2 Combine like terms: 11 + -83 = -72 -72 + -5x + -1x + 10x2 + -9x2 = 83 + x + 9x2 + -83 + -1x + -9x2 Combine like terms: -5x + -1x = -6x -72 + -6x + 10x2 + -9x2 = 83 + x + 9x2 + -83 + -1x + -9x2 Combine like terms: 10x2 + -9x2 = 1x2 -72 + -6x + 1x2 = 83 + x + 9x2 + -83 + -1x + -9x2 Reorder the terms: -72 + -6x + 1x2 = 83 + -83 + x + -1x + 9x2 + -9x2 Combine like terms: 83 + -83 = 0 -72 + -6x + 1x2 = 0 + x + -1x + 9x2 + -9x2 -72 + -6x + 1x2 = x + -1x + 9x2 + -9x2 Combine like terms: x + -1x = 0 -72 + -6x + 1x2 = 0 + 9x2 + -9x2 -72 + -6x + 1x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -72 + -6x + 1x2 = 0 Factor a trinomial. (-6 + -1x)(12 + -1x) = 0Subproblem 1
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 = -6Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12Solution
x = {-6, 12}
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