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Simplifying v2 + 8v + -64 = -4 Reorder the terms: -64 + 8v + v2 = -4 Solving -64 + 8v + v2 = -4 Solving for variable 'v'. Reorder the terms: -64 + 4 + 8v + v2 = -4 + 4 Combine like terms: -64 + 4 = -60 -60 + 8v + v2 = -4 + 4 Combine like terms: -4 + 4 = 0 -60 + 8v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 8v + 60 + v2 = 0 + 60 Reorder the terms: -60 + 60 + 8v + v2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 8v + v2 = 0 + 60 8v + v2 = 0 + 60 Combine like terms: 0 + 60 = 60 8v + v2 = 60 The v term is 8v. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8v + 16 + v2 = 60 + 16 Reorder the terms: 16 + 8v + v2 = 60 + 16 Combine like terms: 60 + 16 = 76 16 + 8v + v2 = 76 Factor a perfect square on the left side: (v + 4)(v + 4) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (v + 4) equal to 8.717797887 and -8.717797887.Subproblem 1
v + 4 = 8.717797887 Simplifying v + 4 = 8.717797887 Reorder the terms: 4 + v = 8.717797887 Solving 4 + v = 8.717797887 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + v = 8.717797887 + -4 Combine like terms: 4 + -4 = 0 0 + v = 8.717797887 + -4 v = 8.717797887 + -4 Combine like terms: 8.717797887 + -4 = 4.717797887 v = 4.717797887 Simplifying v = 4.717797887Subproblem 2
v + 4 = -8.717797887 Simplifying v + 4 = -8.717797887 Reorder the terms: 4 + v = -8.717797887 Solving 4 + v = -8.717797887 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + v = -8.717797887 + -4 Combine like terms: 4 + -4 = 0 0 + v = -8.717797887 + -4 v = -8.717797887 + -4 Combine like terms: -8.717797887 + -4 = -12.717797887 v = -12.717797887 Simplifying v = -12.717797887Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.717797887, -12.717797887}
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