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Simplifying 10x + -2 = 2x2 + 6x Reorder the terms: -2 + 10x = 2x2 + 6x Reorder the terms: -2 + 10x = 6x + 2x2 Solving -2 + 10x = 6x + 2x2 Solving for variable 'x'. Combine like terms: 10x + -6x = 4x -2 + 4x + -2x2 = 6x + 2x2 + -6x + -2x2 Reorder the terms: -2 + 4x + -2x2 = 6x + -6x + 2x2 + -2x2 Combine like terms: 6x + -6x = 0 -2 + 4x + -2x2 = 0 + 2x2 + -2x2 -2 + 4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -2 + 4x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 2x + -1x2) = 0 Factor a trinomial. 2((-1 + x)(1 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1Subproblem 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 = {1, 1}
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