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Simplifying 4x2 + -4x + 2 = x2 + 6x + 10 Reorder the terms: 2 + -4x + 4x2 = x2 + 6x + 10 Reorder the terms: 2 + -4x + 4x2 = 10 + 6x + x2 Solving 2 + -4x + 4x2 = 10 + 6x + x2 Solving for variable 'x'. Reorder the terms: 2 + -10 + -4x + -6x + 4x2 + -1x2 = 10 + 6x + x2 + -10 + -6x + -1x2 Combine like terms: 2 + -10 = -8 -8 + -4x + -6x + 4x2 + -1x2 = 10 + 6x + x2 + -10 + -6x + -1x2 Combine like terms: -4x + -6x = -10x -8 + -10x + 4x2 + -1x2 = 10 + 6x + x2 + -10 + -6x + -1x2 Combine like terms: 4x2 + -1x2 = 3x2 -8 + -10x + 3x2 = 10 + 6x + x2 + -10 + -6x + -1x2 Reorder the terms: -8 + -10x + 3x2 = 10 + -10 + 6x + -6x + x2 + -1x2 Combine like terms: 10 + -10 = 0 -8 + -10x + 3x2 = 0 + 6x + -6x + x2 + -1x2 -8 + -10x + 3x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 -8 + -10x + 3x2 = 0 + x2 + -1x2 -8 + -10x + 3x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -8 + -10x + 3x2 = 0 Factor a trinomial. (-2 + -3x)(4 + -1x) = 0Subproblem 1
Set the factor '(-2 + -3x)' equal to zero and attempt to solve: Simplifying -2 + -3x = 0 Solving -2 + -3x = 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 + -3x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3x = 0 + 2 -3x = 0 + 2 Combine like terms: 0 + 2 = 2 -3x = 2 Divide each side by '-3'. x = -0.6666666667 Simplifying x = -0.6666666667Subproblem 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 = {-0.6666666667, 4}
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