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Simplifying v2 + 110v + -6020 = 0 Reorder the terms: -6020 + 110v + v2 = 0 Solving -6020 + 110v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '6020' to each side of the equation. -6020 + 110v + 6020 + v2 = 0 + 6020 Reorder the terms: -6020 + 6020 + 110v + v2 = 0 + 6020 Combine like terms: -6020 + 6020 = 0 0 + 110v + v2 = 0 + 6020 110v + v2 = 0 + 6020 Combine like terms: 0 + 6020 = 6020 110v + v2 = 6020 The v term is 110v. Take half its coefficient (55). Square it (3025) and add it to both sides. Add '3025' to each side of the equation. 110v + 3025 + v2 = 6020 + 3025 Reorder the terms: 3025 + 110v + v2 = 6020 + 3025 Combine like terms: 6020 + 3025 = 9045 3025 + 110v + v2 = 9045 Factor a perfect square on the left side: (v + 55)(v + 55) = 9045 Calculate the square root of the right side: 95.105204905 Break this problem into two subproblems by setting (v + 55) equal to 95.105204905 and -95.105204905.Subproblem 1
v + 55 = 95.105204905 Simplifying v + 55 = 95.105204905 Reorder the terms: 55 + v = 95.105204905 Solving 55 + v = 95.105204905 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-55' to each side of the equation. 55 + -55 + v = 95.105204905 + -55 Combine like terms: 55 + -55 = 0 0 + v = 95.105204905 + -55 v = 95.105204905 + -55 Combine like terms: 95.105204905 + -55 = 40.105204905 v = 40.105204905 Simplifying v = 40.105204905Subproblem 2
v + 55 = -95.105204905 Simplifying v + 55 = -95.105204905 Reorder the terms: 55 + v = -95.105204905 Solving 55 + v = -95.105204905 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-55' to each side of the equation. 55 + -55 + v = -95.105204905 + -55 Combine like terms: 55 + -55 = 0 0 + v = -95.105204905 + -55 v = -95.105204905 + -55 Combine like terms: -95.105204905 + -55 = -150.105204905 v = -150.105204905 Simplifying v = -150.105204905Solution
The solution to the problem is based on the solutions from the subproblems. v = {40.105204905, -150.105204905}
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