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Simplifying x2 + 16x + 64 = 289 + -34x + x2 + x2 Reorder the terms: 64 + 16x + x2 = 289 + -34x + x2 + x2 Combine like terms: x2 + x2 = 2x2 64 + 16x + x2 = 289 + -34x + 2x2 Solving 64 + 16x + x2 = 289 + -34x + 2x2 Solving for variable 'x'. Reorder the terms: 64 + -289 + 16x + 34x + x2 + -2x2 = 289 + -34x + 2x2 + -289 + 34x + -2x2 Combine like terms: 64 + -289 = -225 -225 + 16x + 34x + x2 + -2x2 = 289 + -34x + 2x2 + -289 + 34x + -2x2 Combine like terms: 16x + 34x = 50x -225 + 50x + x2 + -2x2 = 289 + -34x + 2x2 + -289 + 34x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -225 + 50x + -1x2 = 289 + -34x + 2x2 + -289 + 34x + -2x2 Reorder the terms: -225 + 50x + -1x2 = 289 + -289 + -34x + 34x + 2x2 + -2x2 Combine like terms: 289 + -289 = 0 -225 + 50x + -1x2 = 0 + -34x + 34x + 2x2 + -2x2 -225 + 50x + -1x2 = -34x + 34x + 2x2 + -2x2 Combine like terms: -34x + 34x = 0 -225 + 50x + -1x2 = 0 + 2x2 + -2x2 -225 + 50x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -225 + 50x + -1x2 = 0 Factor a trinomial. (-45 + x)(5 + -1x) = 0Subproblem 1
Set the factor '(-45 + x)' equal to zero and attempt to solve: Simplifying -45 + x = 0 Solving -45 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = 0 + 45 Combine like terms: -45 + 45 = 0 0 + x = 0 + 45 x = 0 + 45 Combine like terms: 0 + 45 = 45 x = 45 Simplifying x = 45Subproblem 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 = {45, 5}
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