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Simplifying v2 + 16v + -12 = 0 Reorder the terms: -12 + 16v + v2 = 0 Solving -12 + 16v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 16v + 12 + v2 = 0 + 12 Reorder the terms: -12 + 12 + 16v + v2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 16v + v2 = 0 + 12 16v + v2 = 0 + 12 Combine like terms: 0 + 12 = 12 16v + v2 = 12 The v term is 16v. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16v + 64 + v2 = 12 + 64 Reorder the terms: 64 + 16v + v2 = 12 + 64 Combine like terms: 12 + 64 = 76 64 + 16v + v2 = 76 Factor a perfect square on the left side: (v + 8)(v + 8) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (v + 8) equal to 8.717797887 and -8.717797887.Subproblem 1
v + 8 = 8.717797887 Simplifying v + 8 = 8.717797887 Reorder the terms: 8 + v = 8.717797887 Solving 8 + v = 8.717797887 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + v = 8.717797887 + -8 Combine like terms: 8 + -8 = 0 0 + v = 8.717797887 + -8 v = 8.717797887 + -8 Combine like terms: 8.717797887 + -8 = 0.717797887 v = 0.717797887 Simplifying v = 0.717797887Subproblem 2
v + 8 = -8.717797887 Simplifying v + 8 = -8.717797887 Reorder the terms: 8 + v = -8.717797887 Solving 8 + v = -8.717797887 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + v = -8.717797887 + -8 Combine like terms: 8 + -8 = 0 0 + v = -8.717797887 + -8 v = -8.717797887 + -8 Combine like terms: -8.717797887 + -8 = -16.717797887 v = -16.717797887 Simplifying v = -16.717797887Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.717797887, -16.717797887}
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