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Simplifying -3v(-8u2 + -8uv + -7v2) = 0 Reorder the terms: -3v(-8uv + -8u2 + -7v2) = 0 (-8uv * -3v + -8u2 * -3v + -7v2 * -3v) = 0 (24uv2 + 24u2v + 21v3) = 0 Solving 24uv2 + 24u2v + 21v3 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '3v'. 3v(8uv + 8u2 + 7v2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'v' equal to zero and attempt to solve: Simplifying v = 0 Solving v = 0 Move all terms containing u to the left, all other terms to the right. Add '-1v' to each side of the equation. v + -1v = 0 + -1v Remove the zero: 0 = -1v Simplifying 0 = -1v 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 '(8uv + 8u2 + 7v2)' equal to zero and attempt to solve: Simplifying 8uv + 8u2 + 7v2 = 0 Solving 8uv + 8u2 + 7v2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. uv + u2 + 0.875v2 = 0 Move the constant term to the right: Add '-0.875v2' to each side of the equation. uv + u2 + 0.875v2 + -0.875v2 = 0 + -0.875v2 Combine like terms: 0.875v2 + -0.875v2 = 0.000 uv + u2 + 0.000 = 0 + -0.875v2 uv + u2 = 0 + -0.875v2 Remove the zero: uv + u2 = -0.875v2 The u term is uv. Take half its coefficient (0.5v). Square it (0.25v2) and add it to both sides. Add '0.25v2' to each side of the equation. v2 + u2 + 0.25v2 = -0.875v2 + 0.25v2 Reorder the terms: u2 + v2 + 0.25v2 = -0.875v2 + 0.25v2 Combine like terms: v2 + 0.25v2 = 1.25v2 u2 + 1.25v2 = -0.875v2 + 0.25v2 Combine like terms: -0.875v2 + 0.25v2 = -0.625v2 u2 + 1.25v2 = -0.625v2 Factor a perfect square on the left side: (u + 0.5v)(u + 0.5v) = -0.625v2 Can't calculate square root of the right side. 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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