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Simplifying 2v * 2v + -10v + 13 = v + -1v + -1 Reorder the terms for easier multiplication: 2 * 2v * v + -10v + 13 = v + -1v + -1 Multiply 2 * 2 4v * v + -10v + 13 = v + -1v + -1 Multiply v * v 4v2 + -10v + 13 = v + -1v + -1 Reorder the terms: 13 + -10v + 4v2 = v + -1v + -1 Reorder the terms: 13 + -10v + 4v2 = -1 + v + -1v Combine like terms: v + -1v = 0 13 + -10v + 4v2 = -1 + 0 13 + -10v + 4v2 = -1 Solving 13 + -10v + 4v2 = -1 Solving for variable 'v'. Reorder the terms: 13 + 1 + -10v + 4v2 = -1 + 1 Combine like terms: 13 + 1 = 14 14 + -10v + 4v2 = -1 + 1 Combine like terms: -1 + 1 = 0 14 + -10v + 4v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -5v + 2v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -5v + 2v2)' equal to zero and attempt to solve: Simplifying 7 + -5v + 2v2 = 0 Solving 7 + -5v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + -2.5v + v2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -2.5v + -3.5 + v2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -2.5v + v2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -2.5v + v2 = 0 + -3.5 -2.5v + v2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -2.5v + v2 = -3.5 The v term is -2.5v. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5v + 1.5625 + v2 = -3.5 + 1.5625 Reorder the terms: 1.5625 + -2.5v + v2 = -3.5 + 1.5625 Combine like terms: -3.5 + 1.5625 = -1.9375 1.5625 + -2.5v + v2 = -1.9375 Factor a perfect square on the left side: (v + -1.25)(v + -1.25) = -1.9375 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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