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Simplifying (v + 6) = 2v2 + 6v + 29 Reorder the terms: (6 + v) = 2v2 + 6v + 29 Remove parenthesis around (6 + v) 6 + v = 2v2 + 6v + 29 Reorder the terms: 6 + v = 29 + 6v + 2v2 Solving 6 + v = 29 + 6v + 2v2 Solving for variable 'v'. Reorder the terms: 6 + -29 + v + -6v + -2v2 = 29 + 6v + 2v2 + -29 + -6v + -2v2 Combine like terms: 6 + -29 = -23 -23 + v + -6v + -2v2 = 29 + 6v + 2v2 + -29 + -6v + -2v2 Combine like terms: v + -6v = -5v -23 + -5v + -2v2 = 29 + 6v + 2v2 + -29 + -6v + -2v2 Reorder the terms: -23 + -5v + -2v2 = 29 + -29 + 6v + -6v + 2v2 + -2v2 Combine like terms: 29 + -29 = 0 -23 + -5v + -2v2 = 0 + 6v + -6v + 2v2 + -2v2 -23 + -5v + -2v2 = 6v + -6v + 2v2 + -2v2 Combine like terms: 6v + -6v = 0 -23 + -5v + -2v2 = 0 + 2v2 + -2v2 -23 + -5v + -2v2 = 2v2 + -2v2 Combine like terms: 2v2 + -2v2 = 0 -23 + -5v + -2v2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(23 + 5v + 2v2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(23 + 5v + 2v2)' equal to zero and attempt to solve: Simplifying 23 + 5v + 2v2 = 0 Solving 23 + 5v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 11.5 + 2.5v + v2 = 0 Move the constant term to the right: Add '-11.5' to each side of the equation. 11.5 + 2.5v + -11.5 + v2 = 0 + -11.5 Reorder the terms: 11.5 + -11.5 + 2.5v + v2 = 0 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + 2.5v + v2 = 0 + -11.5 2.5v + v2 = 0 + -11.5 Combine like terms: 0 + -11.5 = -11.5 2.5v + v2 = -11.5 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 = -11.5 + 1.5625 Reorder the terms: 1.5625 + 2.5v + v2 = -11.5 + 1.5625 Combine like terms: -11.5 + 1.5625 = -9.9375 1.5625 + 2.5v + v2 = -9.9375 Factor a perfect square on the left side: (v + 1.25)(v + 1.25) = -9.9375 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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