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Simplifying -8v2 = 8 + 2v Solving -8v2 = 8 + 2v Solving for variable 'v'. Reorder the terms: -8 + -2v + -8v2 = 8 + 2v + -8 + -2v Reorder the terms: -8 + -2v + -8v2 = 8 + -8 + 2v + -2v Combine like terms: 8 + -8 = 0 -8 + -2v + -8v2 = 0 + 2v + -2v -8 + -2v + -8v2 = 2v + -2v Combine like terms: 2v + -2v = 0 -8 + -2v + -8v2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(4 + v + 4v2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(4 + v + 4v2)' equal to zero and attempt to solve: Simplifying 4 + v + 4v2 = 0 Solving 4 + v + 4v2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1 + 0.25v + v2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 0.25v + -1 + v2 = 0 + -1 Reorder the terms: 1 + -1 + 0.25v + v2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 0.25v + v2 = 0 + -1 0.25v + v2 = 0 + -1 Combine like terms: 0 + -1 = -1 0.25v + v2 = -1 The v term is v. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.25v + 0.25 + v2 = -1 + 0.25 Reorder the terms: 0.25 + 0.25v + v2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + 0.25v + v2 = -0.75 Factor a perfect square on the left side: (v + 0.5)(v + 0.5) = -0.75 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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