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Simplifying 2x2 + 14x + 49 = x2 + 16x + 64 Reorder the terms: 49 + 14x + 2x2 = x2 + 16x + 64 Reorder the terms: 49 + 14x + 2x2 = 64 + 16x + x2 Solving 49 + 14x + 2x2 = 64 + 16x + x2 Solving for variable 'x'. Reorder the terms: 49 + -64 + 14x + -16x + 2x2 + -1x2 = 64 + 16x + x2 + -64 + -16x + -1x2 Combine like terms: 49 + -64 = -15 -15 + 14x + -16x + 2x2 + -1x2 = 64 + 16x + x2 + -64 + -16x + -1x2 Combine like terms: 14x + -16x = -2x -15 + -2x + 2x2 + -1x2 = 64 + 16x + x2 + -64 + -16x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -15 + -2x + 1x2 = 64 + 16x + x2 + -64 + -16x + -1x2 Reorder the terms: -15 + -2x + 1x2 = 64 + -64 + 16x + -16x + x2 + -1x2 Combine like terms: 64 + -64 = 0 -15 + -2x + 1x2 = 0 + 16x + -16x + x2 + -1x2 -15 + -2x + 1x2 = 16x + -16x + x2 + -1x2 Combine like terms: 16x + -16x = 0 -15 + -2x + 1x2 = 0 + x2 + -1x2 -15 + -2x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -15 + -2x + 1x2 = 0 Factor a trinomial. (-3 + -1x)(5 + -1x) = 0Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 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 = {-3, 5}
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