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Simplifying 4x = x2 + -6x + 9 Reorder the terms: 4x = 9 + -6x + x2 Solving 4x = 9 + -6x + x2 Solving for variable 'x'. Reorder the terms: -9 + 4x + 6x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2 Combine like terms: 4x + 6x = 10x -9 + 10x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2 Reorder the terms: -9 + 10x + -1x2 = 9 + -9 + -6x + 6x + x2 + -1x2 Combine like terms: 9 + -9 = 0 -9 + 10x + -1x2 = 0 + -6x + 6x + x2 + -1x2 -9 + 10x + -1x2 = -6x + 6x + x2 + -1x2 Combine like terms: -6x + 6x = 0 -9 + 10x + -1x2 = 0 + x2 + -1x2 -9 + 10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -9 + 10x + -1x2 = 0 Factor a trinomial. (-9 + x)(1 + -1x) = 0Subproblem 1
Set the factor '(-9 + x)' equal to zero and attempt to solve: Simplifying -9 + x = 0 Solving -9 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + x = 0 + 9 x = 0 + 9 Combine like terms: 0 + 9 = 9 x = 9 Simplifying x = 9Subproblem 2
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 = 1Solution
x = {9, 1}
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