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Simplifying v2 + 16v = 65 Reorder the terms: 16v + v2 = 65 Solving 16v + v2 = 65 Solving for variable 'v'. Reorder the terms: -65 + 16v + v2 = 65 + -65 Combine like terms: 65 + -65 = 0 -65 + 16v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '65' to each side of the equation. -65 + 16v + 65 + v2 = 0 + 65 Reorder the terms: -65 + 65 + 16v + v2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + 16v + v2 = 0 + 65 16v + v2 = 0 + 65 Combine like terms: 0 + 65 = 65 16v + v2 = 65 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 = 65 + 64 Reorder the terms: 64 + 16v + v2 = 65 + 64 Combine like terms: 65 + 64 = 129 64 + 16v + v2 = 129 Factor a perfect square on the left side: (v + 8)(v + 8) = 129 Calculate the square root of the right side: 11.357816692 Break this problem into two subproblems by setting (v + 8) equal to 11.357816692 and -11.357816692.Subproblem 1
v + 8 = 11.357816692 Simplifying v + 8 = 11.357816692 Reorder the terms: 8 + v = 11.357816692 Solving 8 + v = 11.357816692 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 = 11.357816692 + -8 Combine like terms: 8 + -8 = 0 0 + v = 11.357816692 + -8 v = 11.357816692 + -8 Combine like terms: 11.357816692 + -8 = 3.357816692 v = 3.357816692 Simplifying v = 3.357816692Subproblem 2
v + 8 = -11.357816692 Simplifying v + 8 = -11.357816692 Reorder the terms: 8 + v = -11.357816692 Solving 8 + v = -11.357816692 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 = -11.357816692 + -8 Combine like terms: 8 + -8 = 0 0 + v = -11.357816692 + -8 v = -11.357816692 + -8 Combine like terms: -11.357816692 + -8 = -19.357816692 v = -19.357816692 Simplifying v = -19.357816692Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.357816692, -19.357816692}
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