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Simplifying 3x + -11 = x2 + -14x + 49 Reorder the terms: -11 + 3x = x2 + -14x + 49 Reorder the terms: -11 + 3x = 49 + -14x + x2 Solving -11 + 3x = 49 + -14x + x2 Solving for variable 'x'. Reorder the terms: -11 + -49 + 3x + 14x + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2 Combine like terms: -11 + -49 = -60 -60 + 3x + 14x + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2 Combine like terms: 3x + 14x = 17x -60 + 17x + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2 Reorder the terms: -60 + 17x + -1x2 = 49 + -49 + -14x + 14x + x2 + -1x2 Combine like terms: 49 + -49 = 0 -60 + 17x + -1x2 = 0 + -14x + 14x + x2 + -1x2 -60 + 17x + -1x2 = -14x + 14x + x2 + -1x2 Combine like terms: -14x + 14x = 0 -60 + 17x + -1x2 = 0 + x2 + -1x2 -60 + 17x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -60 + 17x + -1x2 = 0 Factor a trinomial. (-12 + x)(5 + -1x) = 0Subproblem 1
Set the factor '(-12 + x)' equal to zero and attempt to solve: Simplifying -12 + x = 0 Solving -12 + x = 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 + x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + x = 0 + 12 x = 0 + 12 Combine like terms: 0 + 12 = 12 x = 12 Simplifying x = 12Subproblem 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 = {12, 5}
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