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Simplifying 8v2 + -16v = 58 Reorder the terms: -16v + 8v2 = 58 Solving -16v + 8v2 = 58 Solving for variable 'v'. Reorder the terms: -58 + -16v + 8v2 = 58 + -58 Combine like terms: 58 + -58 = 0 -58 + -16v + 8v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-29 + -8v + 4v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-29 + -8v + 4v2)' equal to zero and attempt to solve: Simplifying -29 + -8v + 4v2 = 0 Solving -29 + -8v + 4v2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7.25 + -2v + v2 = 0 Move the constant term to the right: Add '7.25' to each side of the equation. -7.25 + -2v + 7.25 + v2 = 0 + 7.25 Reorder the terms: -7.25 + 7.25 + -2v + v2 = 0 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + -2v + v2 = 0 + 7.25 -2v + v2 = 0 + 7.25 Combine like terms: 0 + 7.25 = 7.25 -2v + v2 = 7.25 The v term is -2v. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2v + 1 + v2 = 7.25 + 1 Reorder the terms: 1 + -2v + v2 = 7.25 + 1 Combine like terms: 7.25 + 1 = 8.25 1 + -2v + v2 = 8.25 Factor a perfect square on the left side: (v + -1)(v + -1) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (v + -1) equal to 2.872281323 and -2.872281323.Subproblem 1
v + -1 = 2.872281323 Simplifying v + -1 = 2.872281323 Reorder the terms: -1 + v = 2.872281323 Solving -1 + v = 2.872281323 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + v = 2.872281323 + 1 Combine like terms: -1 + 1 = 0 0 + v = 2.872281323 + 1 v = 2.872281323 + 1 Combine like terms: 2.872281323 + 1 = 3.872281323 v = 3.872281323 Simplifying v = 3.872281323Subproblem 2
v + -1 = -2.872281323 Simplifying v + -1 = -2.872281323 Reorder the terms: -1 + v = -2.872281323 Solving -1 + v = -2.872281323 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + v = -2.872281323 + 1 Combine like terms: -1 + 1 = 0 0 + v = -2.872281323 + 1 v = -2.872281323 + 1 Combine like terms: -2.872281323 + 1 = -1.872281323 v = -1.872281323 Simplifying v = -1.872281323Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.872281323, -1.872281323}Solution
v = {3.872281323, -1.872281323}
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