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Simplifying v2 + 10v = 17 Reorder the terms: 10v + v2 = 17 Solving 10v + v2 = 17 Solving for variable 'v'. Reorder the terms: -17 + 10v + v2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + 10v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 10v + 17 + v2 = 0 + 17 Reorder the terms: -17 + 17 + 10v + v2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 10v + v2 = 0 + 17 10v + v2 = 0 + 17 Combine like terms: 0 + 17 = 17 10v + v2 = 17 The v term is 10v. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10v + 25 + v2 = 17 + 25 Reorder the terms: 25 + 10v + v2 = 17 + 25 Combine like terms: 17 + 25 = 42 25 + 10v + v2 = 42 Factor a perfect square on the left side: (v + 5)(v + 5) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (v + 5) equal to 6.480740698 and -6.480740698.Subproblem 1
v + 5 = 6.480740698 Simplifying v + 5 = 6.480740698 Reorder the terms: 5 + v = 6.480740698 Solving 5 + v = 6.480740698 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + v = 6.480740698 + -5 Combine like terms: 5 + -5 = 0 0 + v = 6.480740698 + -5 v = 6.480740698 + -5 Combine like terms: 6.480740698 + -5 = 1.480740698 v = 1.480740698 Simplifying v = 1.480740698Subproblem 2
v + 5 = -6.480740698 Simplifying v + 5 = -6.480740698 Reorder the terms: 5 + v = -6.480740698 Solving 5 + v = -6.480740698 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + v = -6.480740698 + -5 Combine like terms: 5 + -5 = 0 0 + v = -6.480740698 + -5 v = -6.480740698 + -5 Combine like terms: -6.480740698 + -5 = -11.480740698 v = -11.480740698 Simplifying v = -11.480740698Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.480740698, -11.480740698}
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