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Simplifying (v2 + -4v + -7) = (5v2 + -3v + 6) Reorder the terms: (-7 + -4v + v2) = (5v2 + -3v + 6) Remove parenthesis around (-7 + -4v + v2) -7 + -4v + v2 = (5v2 + -3v + 6) Reorder the terms: -7 + -4v + v2 = (6 + -3v + 5v2) Remove parenthesis around (6 + -3v + 5v2) -7 + -4v + v2 = 6 + -3v + 5v2 Solving -7 + -4v + v2 = 6 + -3v + 5v2 Solving for variable 'v'. Reorder the terms: -7 + -6 + -4v + 3v + v2 + -5v2 = 6 + -3v + 5v2 + -6 + 3v + -5v2 Combine like terms: -7 + -6 = -13 -13 + -4v + 3v + v2 + -5v2 = 6 + -3v + 5v2 + -6 + 3v + -5v2 Combine like terms: -4v + 3v = -1v -13 + -1v + v2 + -5v2 = 6 + -3v + 5v2 + -6 + 3v + -5v2 Combine like terms: v2 + -5v2 = -4v2 -13 + -1v + -4v2 = 6 + -3v + 5v2 + -6 + 3v + -5v2 Reorder the terms: -13 + -1v + -4v2 = 6 + -6 + -3v + 3v + 5v2 + -5v2 Combine like terms: 6 + -6 = 0 -13 + -1v + -4v2 = 0 + -3v + 3v + 5v2 + -5v2 -13 + -1v + -4v2 = -3v + 3v + 5v2 + -5v2 Combine like terms: -3v + 3v = 0 -13 + -1v + -4v2 = 0 + 5v2 + -5v2 -13 + -1v + -4v2 = 5v2 + -5v2 Combine like terms: 5v2 + -5v2 = 0 -13 + -1v + -4v2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(13 + v + 4v2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(13 + v + 4v2)' equal to zero and attempt to solve: Simplifying 13 + v + 4v2 = 0 Solving 13 + v + 4v2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.25 + 0.25v + v2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + 0.25v + -3.25 + v2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + 0.25v + v2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + 0.25v + v2 = 0 + -3.25 0.25v + v2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 0.25v + v2 = -3.25 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 = -3.25 + 0.25 Reorder the terms: 0.25 + 0.25v + v2 = -3.25 + 0.25 Combine like terms: -3.25 + 0.25 = -3 0.25 + 0.25v + v2 = -3 Factor a perfect square on the left side: (v + 0.5)(v + 0.5) = -3 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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