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Simplifying 4 + -1x = x2 + -6x + 10 Reorder the terms: 4 + -1x = 10 + -6x + x2 Solving 4 + -1x = 10 + -6x + x2 Solving for variable 'x'. Reorder the terms: 4 + -10 + -1x + 6x + -1x2 = 10 + -6x + x2 + -10 + 6x + -1x2 Combine like terms: 4 + -10 = -6 -6 + -1x + 6x + -1x2 = 10 + -6x + x2 + -10 + 6x + -1x2 Combine like terms: -1x + 6x = 5x -6 + 5x + -1x2 = 10 + -6x + x2 + -10 + 6x + -1x2 Reorder the terms: -6 + 5x + -1x2 = 10 + -10 + -6x + 6x + x2 + -1x2 Combine like terms: 10 + -10 = 0 -6 + 5x + -1x2 = 0 + -6x + 6x + x2 + -1x2 -6 + 5x + -1x2 = -6x + 6x + x2 + -1x2 Combine like terms: -6x + 6x = 0 -6 + 5x + -1x2 = 0 + x2 + -1x2 -6 + 5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -6 + 5x + -1x2 = 0 Factor a trinomial. (-3 + x)(2 + -1x) = 0Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {3, 2}
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