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Simplifying v2 + 44v + -1000 = 0 Reorder the terms: -1000 + 44v + v2 = 0 Solving -1000 + 44v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '1000' to each side of the equation. -1000 + 44v + 1000 + v2 = 0 + 1000 Reorder the terms: -1000 + 1000 + 44v + v2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + 44v + v2 = 0 + 1000 44v + v2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 44v + v2 = 1000 The v term is 44v. Take half its coefficient (22). Square it (484) and add it to both sides. Add '484' to each side of the equation. 44v + 484 + v2 = 1000 + 484 Reorder the terms: 484 + 44v + v2 = 1000 + 484 Combine like terms: 1000 + 484 = 1484 484 + 44v + v2 = 1484 Factor a perfect square on the left side: (v + 22)(v + 22) = 1484 Calculate the square root of the right side: 38.522720569 Break this problem into two subproblems by setting (v + 22) equal to 38.522720569 and -38.522720569.Subproblem 1
v + 22 = 38.522720569 Simplifying v + 22 = 38.522720569 Reorder the terms: 22 + v = 38.522720569 Solving 22 + v = 38.522720569 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + v = 38.522720569 + -22 Combine like terms: 22 + -22 = 0 0 + v = 38.522720569 + -22 v = 38.522720569 + -22 Combine like terms: 38.522720569 + -22 = 16.522720569 v = 16.522720569 Simplifying v = 16.522720569Subproblem 2
v + 22 = -38.522720569 Simplifying v + 22 = -38.522720569 Reorder the terms: 22 + v = -38.522720569 Solving 22 + v = -38.522720569 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + v = -38.522720569 + -22 Combine like terms: 22 + -22 = 0 0 + v = -38.522720569 + -22 v = -38.522720569 + -22 Combine like terms: -38.522720569 + -22 = -60.522720569 v = -60.522720569 Simplifying v = -60.522720569Solution
The solution to the problem is based on the solutions from the subproblems. v = {16.522720569, -60.522720569}
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