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Simplifying 8sqrt(x2 + 2x) = 8sqrt(2x2 + -1x + -4) Reorder the terms: 8qrst(2x + x2) = 8sqrt(2x2 + -1x + -4) (2x * 8qrst + x2 * 8qrst) = 8sqrt(2x2 + -1x + -4) (16qrstx + 8qrstx2) = 8sqrt(2x2 + -1x + -4) Reorder the terms: 16qrstx + 8qrstx2 = 8qrst(-4 + -1x + 2x2) 16qrstx + 8qrstx2 = (-4 * 8qrst + -1x * 8qrst + 2x2 * 8qrst) 16qrstx + 8qrstx2 = (-32qrst + -8qrstx + 16qrstx2) Solving 16qrstx + 8qrstx2 = -32qrst + -8qrstx + 16qrstx2 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '32qrst' to each side of the equation. 16qrstx + 32qrst + 8qrstx2 = -32qrst + -8qrstx + 32qrst + 16qrstx2 Reorder the terms: 32qrst + 16qrstx + 8qrstx2 = -32qrst + -8qrstx + 32qrst + 16qrstx2 Reorder the terms: 32qrst + 16qrstx + 8qrstx2 = -32qrst + 32qrst + -8qrstx + 16qrstx2 Combine like terms: -32qrst + 32qrst = 0 32qrst + 16qrstx + 8qrstx2 = 0 + -8qrstx + 16qrstx2 32qrst + 16qrstx + 8qrstx2 = -8qrstx + 16qrstx2 Add '8qrstx' to each side of the equation. 32qrst + 16qrstx + 8qrstx + 8qrstx2 = -8qrstx + 8qrstx + 16qrstx2 Combine like terms: 16qrstx + 8qrstx = 24qrstx 32qrst + 24qrstx + 8qrstx2 = -8qrstx + 8qrstx + 16qrstx2 Combine like terms: -8qrstx + 8qrstx = 0 32qrst + 24qrstx + 8qrstx2 = 0 + 16qrstx2 32qrst + 24qrstx + 8qrstx2 = 16qrstx2 Add '-16qrstx2' to each side of the equation. 32qrst + 24qrstx + 8qrstx2 + -16qrstx2 = 16qrstx2 + -16qrstx2 Combine like terms: 8qrstx2 + -16qrstx2 = -8qrstx2 32qrst + 24qrstx + -8qrstx2 = 16qrstx2 + -16qrstx2 Combine like terms: 16qrstx2 + -16qrstx2 = 0 32qrst + 24qrstx + -8qrstx2 = 0 Factor out the Greatest Common Factor (GCF), '8qrst'. 8qrst(4 + 3x + -1x2) = 0 Factor a trinomial. 8qrst((4 + -1x)(1 + x)) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'qrst' equal to zero and attempt to solve: Simplifying qrst = 0 Solving qrst = 0 Move all terms containing q to the left, all other terms to the right. Simplifying qrst = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 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 q 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 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing q 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 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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