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Simplifying (x)(x) + -1x(2x + -10) = (x + -2)(x + -2) + 8 Multiply x * x x2 + -1x(2x + -10) = (x + -2)(x + -2) + 8 Reorder the terms: x2 + -1x(-10 + 2x) = (x + -2)(x + -2) + 8 x2 + (-10 * -1x + 2x * -1x) = (x + -2)(x + -2) + 8 x2 + (10x + -2x2) = (x + -2)(x + -2) + 8 Reorder the terms: 10x + x2 + -2x2 = (x + -2)(x + -2) + 8 Combine like terms: x2 + -2x2 = -1x2 10x + -1x2 = (x + -2)(x + -2) + 8 Reorder the terms: 10x + -1x2 = (-2 + x)(x + -2) + 8 Reorder the terms: 10x + -1x2 = (-2 + x)(-2 + x) + 8 Multiply (-2 + x) * (-2 + x) 10x + -1x2 = (-2(-2 + x) + x(-2 + x)) + 8 10x + -1x2 = ((-2 * -2 + x * -2) + x(-2 + x)) + 8 10x + -1x2 = ((4 + -2x) + x(-2 + x)) + 8 10x + -1x2 = (4 + -2x + (-2 * x + x * x)) + 8 10x + -1x2 = (4 + -2x + (-2x + x2)) + 8 Combine like terms: -2x + -2x = -4x 10x + -1x2 = (4 + -4x + x2) + 8 Reorder the terms: 10x + -1x2 = 4 + 8 + -4x + x2 Combine like terms: 4 + 8 = 12 10x + -1x2 = 12 + -4x + x2 Solving 10x + -1x2 = 12 + -4x + x2 Solving for variable 'x'. Reorder the terms: -12 + 10x + 4x + -1x2 + -1x2 = 12 + -4x + x2 + -12 + 4x + -1x2 Combine like terms: 10x + 4x = 14x -12 + 14x + -1x2 + -1x2 = 12 + -4x + x2 + -12 + 4x + -1x2 Combine like terms: -1x2 + -1x2 = -2x2 -12 + 14x + -2x2 = 12 + -4x + x2 + -12 + 4x + -1x2 Reorder the terms: -12 + 14x + -2x2 = 12 + -12 + -4x + 4x + x2 + -1x2 Combine like terms: 12 + -12 = 0 -12 + 14x + -2x2 = 0 + -4x + 4x + x2 + -1x2 -12 + 14x + -2x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 -12 + 14x + -2x2 = 0 + x2 + -1x2 -12 + 14x + -2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 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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