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Simplifying x2 + 6x + 1 = 9x + 5 Reorder the terms: 1 + 6x + x2 = 9x + 5 Reorder the terms: 1 + 6x + x2 = 5 + 9x Solving 1 + 6x + x2 = 5 + 9x Solving for variable 'x'. Reorder the terms: 1 + -5 + 6x + -9x + x2 = 5 + 9x + -5 + -9x Combine like terms: 1 + -5 = -4 -4 + 6x + -9x + x2 = 5 + 9x + -5 + -9x Combine like terms: 6x + -9x = -3x -4 + -3x + x2 = 5 + 9x + -5 + -9x Reorder the terms: -4 + -3x + x2 = 5 + -5 + 9x + -9x Combine like terms: 5 + -5 = 0 -4 + -3x + x2 = 0 + 9x + -9x -4 + -3x + x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -4 + -3x + x2 = 0 Factor a trinomial. (-1 + -1x)(4 + -1x) = 0Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 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 = {-1, 4}
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