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Simplifying x2 + 4x + -6 = -1x2 + 5x + 4 Reorder the terms: -6 + 4x + x2 = -1x2 + 5x + 4 Reorder the terms: -6 + 4x + x2 = 4 + 5x + -1x2 Solving -6 + 4x + x2 = 4 + 5x + -1x2 Solving for variable 'x'. Reorder the terms: -6 + -4 + 4x + -5x + x2 + x2 = 4 + 5x + -1x2 + -4 + -5x + x2 Combine like terms: -6 + -4 = -10 -10 + 4x + -5x + x2 + x2 = 4 + 5x + -1x2 + -4 + -5x + x2 Combine like terms: 4x + -5x = -1x -10 + -1x + x2 + x2 = 4 + 5x + -1x2 + -4 + -5x + x2 Combine like terms: x2 + x2 = 2x2 -10 + -1x + 2x2 = 4 + 5x + -1x2 + -4 + -5x + x2 Reorder the terms: -10 + -1x + 2x2 = 4 + -4 + 5x + -5x + -1x2 + x2 Combine like terms: 4 + -4 = 0 -10 + -1x + 2x2 = 0 + 5x + -5x + -1x2 + x2 -10 + -1x + 2x2 = 5x + -5x + -1x2 + x2 Combine like terms: 5x + -5x = 0 -10 + -1x + 2x2 = 0 + -1x2 + x2 -10 + -1x + 2x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -10 + -1x + 2x2 = 0 Factor a trinomial. (-2 + -1x)(5 + -2x) = 0Subproblem 1
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 = -2Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {-2, 2.5}
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