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Simplifying x2 + -3x + 5 = -1x2 + -7x + 21 Reorder the terms: 5 + -3x + x2 = -1x2 + -7x + 21 Reorder the terms: 5 + -3x + x2 = 21 + -7x + -1x2 Solving 5 + -3x + x2 = 21 + -7x + -1x2 Solving for variable 'x'. Reorder the terms: 5 + -21 + -3x + 7x + x2 + x2 = 21 + -7x + -1x2 + -21 + 7x + x2 Combine like terms: 5 + -21 = -16 -16 + -3x + 7x + x2 + x2 = 21 + -7x + -1x2 + -21 + 7x + x2 Combine like terms: -3x + 7x = 4x -16 + 4x + x2 + x2 = 21 + -7x + -1x2 + -21 + 7x + x2 Combine like terms: x2 + x2 = 2x2 -16 + 4x + 2x2 = 21 + -7x + -1x2 + -21 + 7x + x2 Reorder the terms: -16 + 4x + 2x2 = 21 + -21 + -7x + 7x + -1x2 + x2 Combine like terms: 21 + -21 = 0 -16 + 4x + 2x2 = 0 + -7x + 7x + -1x2 + x2 -16 + 4x + 2x2 = -7x + 7x + -1x2 + x2 Combine like terms: -7x + 7x = 0 -16 + 4x + 2x2 = 0 + -1x2 + x2 -16 + 4x + 2x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -16 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 2x + x2) = 0 Factor a trinomial. 2((-4 + -1x)(2 + -1x)) = 0 Ignore the factor 2.Subproblem 1
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 = -4Subproblem 2
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 = 2Solution
x = {-4, 2}
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