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Simplifying 4sqrt(x2 + 2x) = 4sqrt(3) Reorder the terms: 4qrst(2x + x2) = 4sqrt(3) (2x * 4qrst + x2 * 4qrst) = 4sqrt(3) (8qrstx + 4qrstx2) = 4sqrt(3) Reorder the terms for easier multiplication: 8qrstx + 4qrstx2 = 4 * 3qrst Multiply 4 * 3 8qrstx + 4qrstx2 = 12qrst Solving 8qrstx + 4qrstx2 = 12qrst Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-12qrst' to each side of the equation. 8qrstx + -12qrst + 4qrstx2 = 12qrst + -12qrst Reorder the terms: -12qrst + 8qrstx + 4qrstx2 = 12qrst + -12qrst Combine like terms: 12qrst + -12qrst = 0 -12qrst + 8qrstx + 4qrstx2 = 0 Factor out the Greatest Common Factor (GCF), '4qrst'. 4qrst(-3 + 2x + x2) = 0 Factor a trinomial. 4qrst((-3 + -1x)(1 + -1x)) = 0 Ignore the factor 4.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 '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing q to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Add 'x' to each side of the equation. -1x + x = 3 + x Combine like terms: -1x + x = 0 0 = 3 + x Simplifying 0 = 3 + 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 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + x 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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