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Simplifying v2 + -16v + -8 = 0 Reorder the terms: -8 + -16v + v2 = 0 Solving -8 + -16v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -16v + 8 + v2 = 0 + 8 Reorder the terms: -8 + 8 + -16v + v2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -16v + v2 = 0 + 8 -16v + v2 = 0 + 8 Combine like terms: 0 + 8 = 8 -16v + v2 = 8 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 = 8 + 64 Reorder the terms: 64 + -16v + v2 = 8 + 64 Combine like terms: 8 + 64 = 72 64 + -16v + v2 = 72 Factor a perfect square on the left side: (v + -8)(v + -8) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (v + -8) equal to 8.485281374 and -8.485281374.Subproblem 1
v + -8 = 8.485281374 Simplifying v + -8 = 8.485281374 Reorder the terms: -8 + v = 8.485281374 Solving -8 + v = 8.485281374 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 = 8.485281374 + 8 Combine like terms: -8 + 8 = 0 0 + v = 8.485281374 + 8 v = 8.485281374 + 8 Combine like terms: 8.485281374 + 8 = 16.485281374 v = 16.485281374 Simplifying v = 16.485281374Subproblem 2
v + -8 = -8.485281374 Simplifying v + -8 = -8.485281374 Reorder the terms: -8 + v = -8.485281374 Solving -8 + v = -8.485281374 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 = -8.485281374 + 8 Combine like terms: -8 + 8 = 0 0 + v = -8.485281374 + 8 v = -8.485281374 + 8 Combine like terms: -8.485281374 + 8 = -0.485281374 v = -0.485281374 Simplifying v = -0.485281374Solution
The solution to the problem is based on the solutions from the subproblems. v = {16.485281374, -0.485281374}
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