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Simplifying 4x = 2x2 + -10x + 12 Reorder the terms: 4x = 12 + -10x + 2x2 Solving 4x = 12 + -10x + 2x2 Solving for variable 'x'. Reorder the terms: -12 + 4x + 10x + -2x2 = 12 + -10x + 2x2 + -12 + 10x + -2x2 Combine like terms: 4x + 10x = 14x -12 + 14x + -2x2 = 12 + -10x + 2x2 + -12 + 10x + -2x2 Reorder the terms: -12 + 14x + -2x2 = 12 + -12 + -10x + 10x + 2x2 + -2x2 Combine like terms: 12 + -12 = 0 -12 + 14x + -2x2 = 0 + -10x + 10x + 2x2 + -2x2 -12 + 14x + -2x2 = -10x + 10x + 2x2 + -2x2 Combine like terms: -10x + 10x = 0 -12 + 14x + -2x2 = 0 + 2x2 + -2x2 -12 + 14x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -12 + 14x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 7x + -1x2) = 0 Factor a trinomial. 2((-6 + x)(1 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 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 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Subproblem 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 = {6, 1}
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