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Simplifying 2v2 + 24v + -34 = 0 Reorder the terms: -34 + 24v + 2v2 = 0 Solving -34 + 24v + 2v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(-17 + 12v + v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-17 + 12v + v2)' equal to zero and attempt to solve: Simplifying -17 + 12v + v2 = 0 Solving -17 + 12v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 12v + 17 + v2 = 0 + 17 Reorder the terms: -17 + 17 + 12v + v2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 12v + v2 = 0 + 17 12v + v2 = 0 + 17 Combine like terms: 0 + 17 = 17 12v + v2 = 17 The v term is 12v. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12v + 36 + v2 = 17 + 36 Reorder the terms: 36 + 12v + v2 = 17 + 36 Combine like terms: 17 + 36 = 53 36 + 12v + v2 = 53 Factor a perfect square on the left side: (v + 6)(v + 6) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (v + 6) equal to 7.280109889 and -7.280109889.Subproblem 1
v + 6 = 7.280109889 Simplifying v + 6 = 7.280109889 Reorder the terms: 6 + v = 7.280109889 Solving 6 + v = 7.280109889 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + v = 7.280109889 + -6 Combine like terms: 6 + -6 = 0 0 + v = 7.280109889 + -6 v = 7.280109889 + -6 Combine like terms: 7.280109889 + -6 = 1.280109889 v = 1.280109889 Simplifying v = 1.280109889Subproblem 2
v + 6 = -7.280109889 Simplifying v + 6 = -7.280109889 Reorder the terms: 6 + v = -7.280109889 Solving 6 + v = -7.280109889 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + v = -7.280109889 + -6 Combine like terms: 6 + -6 = 0 0 + v = -7.280109889 + -6 v = -7.280109889 + -6 Combine like terms: -7.280109889 + -6 = -13.280109889 v = -13.280109889 Simplifying v = -13.280109889Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.280109889, -13.280109889}Solution
v = {1.280109889, -13.280109889}
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