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Simplifying 0 = sqrt(16x8 + 32x6 + 24x4 + 8x2 + 1) Reorder the terms: 0 = qrst(1 + 8x2 + 24x4 + 32x6 + 16x8) 0 = (1 * qrst + 8x2 * qrst + 24x4 * qrst + 32x6 * qrst + 16x8 * qrst) 0 = (1qrst + 8qrstx2 + 24qrstx4 + 32qrstx6 + 16qrstx8) Solving 0 = 1qrst + 8qrstx2 + 24qrstx4 + 32qrstx6 + 16qrstx8 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1qrst' to each side of the equation. 0 + -1qrst = 1qrst + 8qrstx2 + 24qrstx4 + 32qrstx6 + -1qrst + 16qrstx8 Remove the zero: -1qrst = 1qrst + 8qrstx2 + 24qrstx4 + 32qrstx6 + -1qrst + 16qrstx8 Reorder the terms: -1qrst = 1qrst + -1qrst + 8qrstx2 + 24qrstx4 + 32qrstx6 + 16qrstx8 Combine like terms: 1qrst + -1qrst = 0 -1qrst = 0 + 8qrstx2 + 24qrstx4 + 32qrstx6 + 16qrstx8 -1qrst = 8qrstx2 + 24qrstx4 + 32qrstx6 + 16qrstx8 Add '-8qrstx2' to each side of the equation. -1qrst + -8qrstx2 = 8qrstx2 + 24qrstx4 + 32qrstx6 + -8qrstx2 + 16qrstx8 Reorder the terms: -1qrst + -8qrstx2 = 8qrstx2 + -8qrstx2 + 24qrstx4 + 32qrstx6 + 16qrstx8 Combine like terms: 8qrstx2 + -8qrstx2 = 0 -1qrst + -8qrstx2 = 0 + 24qrstx4 + 32qrstx6 + 16qrstx8 -1qrst + -8qrstx2 = 24qrstx4 + 32qrstx6 + 16qrstx8 Add '-24qrstx4' to each side of the equation. -1qrst + -8qrstx2 + -24qrstx4 = 24qrstx4 + 32qrstx6 + -24qrstx4 + 16qrstx8 Reorder the terms: -1qrst + -8qrstx2 + -24qrstx4 = 24qrstx4 + -24qrstx4 + 32qrstx6 + 16qrstx8 Combine like terms: 24qrstx4 + -24qrstx4 = 0 -1qrst + -8qrstx2 + -24qrstx4 = 0 + 32qrstx6 + 16qrstx8 -1qrst + -8qrstx2 + -24qrstx4 = 32qrstx6 + 16qrstx8 Add '-32qrstx6' to each side of the equation. -1qrst + -8qrstx2 + -24qrstx4 + -32qrstx6 = 32qrstx6 + -32qrstx6 + 16qrstx8 Combine like terms: 32qrstx6 + -32qrstx6 = 0 -1qrst + -8qrstx2 + -24qrstx4 + -32qrstx6 = 0 + 16qrstx8 -1qrst + -8qrstx2 + -24qrstx4 + -32qrstx6 = 16qrstx8 Add '-16qrstx8' to each side of the equation. -1qrst + -8qrstx2 + -24qrstx4 + -32qrstx6 + -16qrstx8 = 16qrstx8 + -16qrstx8 Combine like terms: 16qrstx8 + -16qrstx8 = 0 -1qrst + -8qrstx2 + -24qrstx4 + -32qrstx6 + -16qrstx8 = 0 Factor out the Greatest Common Factor (GCF), '-1qrst'. -1qrst(1 + 8x2 + 24x4 + 32x6 + 16x8) = 0 Ignore the factor -1.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 '(1 + 8x2 + 24x4 + 32x6 + 16x8)' equal to zero and attempt to solve: Simplifying 1 + 8x2 + 24x4 + 32x6 + 16x8 = 0 Solving 1 + 8x2 + 24x4 + 32x6 + 16x8 = 0 Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 8x2 + 24x4 + 32x6 + -1 + 16x8 = 0 + -1 Reorder the terms: 1 + -1 + 8x2 + 24x4 + 32x6 + 16x8 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8x2 + 24x4 + 32x6 + 16x8 = 0 + -1 8x2 + 24x4 + 32x6 + 16x8 = 0 + -1 Combine like terms: 0 + -1 = -1 8x2 + 24x4 + 32x6 + 16x8 = -1 Add '-8x2' to each side of the equation. 8x2 + 24x4 + 32x6 + -8x2 + 16x8 = -1 + -8x2 Reorder the terms: 8x2 + -8x2 + 24x4 + 32x6 + 16x8 = -1 + -8x2 Combine like terms: 8x2 + -8x2 = 0 0 + 24x4 + 32x6 + 16x8 = -1 + -8x2 24x4 + 32x6 + 16x8 = -1 + -8x2 Add '-24x4' to each side of the equation. 24x4 + 32x6 + -24x4 + 16x8 = -1 + -8x2 + -24x4 Reorder the terms: 24x4 + -24x4 + 32x6 + 16x8 = -1 + -8x2 + -24x4 Combine like terms: 24x4 + -24x4 = 0 0 + 32x6 + 16x8 = -1 + -8x2 + -24x4 32x6 + 16x8 = -1 + -8x2 + -24x4 Add '-32x6' to each side of the equation. 32x6 + -32x6 + 16x8 = -1 + -8x2 + -24x4 + -32x6 Combine like terms: 32x6 + -32x6 = 0 0 + 16x8 = -1 + -8x2 + -24x4 + -32x6 16x8 = -1 + -8x2 + -24x4 + -32x6 Add '-16x8' to each side of the equation. 16x8 + -16x8 = -1 + -8x2 + -24x4 + -32x6 + -16x8 Combine like terms: 16x8 + -16x8 = 0 0 = -1 + -8x2 + -24x4 + -32x6 + -16x8 Simplifying 0 = -1 + -8x2 + -24x4 + -32x6 + -16x8 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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