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Simplifying x2 + -4x + 5 = 3x + -1 Reorder the terms: 5 + -4x + x2 = 3x + -1 Reorder the terms: 5 + -4x + x2 = -1 + 3x Solving 5 + -4x + x2 = -1 + 3x Solving for variable 'x'. Reorder the terms: 5 + 1 + -4x + -3x + x2 = -1 + 3x + 1 + -3x Combine like terms: 5 + 1 = 6 6 + -4x + -3x + x2 = -1 + 3x + 1 + -3x Combine like terms: -4x + -3x = -7x 6 + -7x + x2 = -1 + 3x + 1 + -3x Reorder the terms: 6 + -7x + x2 = -1 + 1 + 3x + -3x Combine like terms: -1 + 1 = 0 6 + -7x + x2 = 0 + 3x + -3x 6 + -7x + x2 = 3x + -3x Combine like terms: 3x + -3x = 0 6 + -7x + x2 = 0 Factor a trinomial. (1 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {1, 6}
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