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Simplifying v2 = 14 + 16v Solving v2 = 14 + 16v Solving for variable 'v'. Reorder the terms: -14 + -16v + v2 = 14 + 16v + -14 + -16v Reorder the terms: -14 + -16v + v2 = 14 + -14 + 16v + -16v Combine like terms: 14 + -14 = 0 -14 + -16v + v2 = 0 + 16v + -16v -14 + -16v + v2 = 16v + -16v Combine like terms: 16v + -16v = 0 -14 + -16v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -16v + 14 + v2 = 0 + 14 Reorder the terms: -14 + 14 + -16v + v2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -16v + v2 = 0 + 14 -16v + v2 = 0 + 14 Combine like terms: 0 + 14 = 14 -16v + v2 = 14 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 = 14 + 64 Reorder the terms: 64 + -16v + v2 = 14 + 64 Combine like terms: 14 + 64 = 78 64 + -16v + v2 = 78 Factor a perfect square on the left side: (v + -8)(v + -8) = 78 Calculate the square root of the right side: 8.831760866 Break this problem into two subproblems by setting (v + -8) equal to 8.831760866 and -8.831760866.Subproblem 1
v + -8 = 8.831760866 Simplifying v + -8 = 8.831760866 Reorder the terms: -8 + v = 8.831760866 Solving -8 + v = 8.831760866 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 = 8.831760866 + 8 Combine like terms: -8 + 8 = 0 0 + v = 8.831760866 + 8 v = 8.831760866 + 8 Combine like terms: 8.831760866 + 8 = 16.831760866 v = 16.831760866 Simplifying v = 16.831760866Subproblem 2
v + -8 = -8.831760866 Simplifying v + -8 = -8.831760866 Reorder the terms: -8 + v = -8.831760866 Solving -8 + v = -8.831760866 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 = -8.831760866 + 8 Combine like terms: -8 + 8 = 0 0 + v = -8.831760866 + 8 v = -8.831760866 + 8 Combine like terms: -8.831760866 + 8 = -0.831760866 v = -0.831760866 Simplifying v = -0.831760866Solution
The solution to the problem is based on the solutions from the subproblems. v = {16.831760866, -0.831760866}
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