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Simplifying 2x + 1 = x2 + -14x + 49 Reorder the terms: 1 + 2x = x2 + -14x + 49 Reorder the terms: 1 + 2x = 49 + -14x + x2 Solving 1 + 2x = 49 + -14x + x2 Solving for variable 'x'. Reorder the terms: 1 + -49 + 2x + 14x + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2 Combine like terms: 1 + -49 = -48 -48 + 2x + 14x + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2 Combine like terms: 2x + 14x = 16x -48 + 16x + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2 Reorder the terms: -48 + 16x + -1x2 = 49 + -49 + -14x + 14x + x2 + -1x2 Combine like terms: 49 + -49 = 0 -48 + 16x + -1x2 = 0 + -14x + 14x + x2 + -1x2 -48 + 16x + -1x2 = -14x + 14x + x2 + -1x2 Combine like terms: -14x + 14x = 0 -48 + 16x + -1x2 = 0 + x2 + -1x2 -48 + 16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -48 + 16x + -1x2 = 0 Factor a trinomial. (-12 + x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {12, 4}
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