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Simplifying v2 + 2v = 45 Reorder the terms: 2v + v2 = 45 Solving 2v + v2 = 45 Solving for variable 'v'. Reorder the terms: -45 + 2v + v2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + 2v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 2v + 45 + v2 = 0 + 45 Reorder the terms: -45 + 45 + 2v + v2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 2v + v2 = 0 + 45 2v + v2 = 0 + 45 Combine like terms: 0 + 45 = 45 2v + v2 = 45 The v term is 2v. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2v + 1 + v2 = 45 + 1 Reorder the terms: 1 + 2v + v2 = 45 + 1 Combine like terms: 45 + 1 = 46 1 + 2v + v2 = 46 Factor a perfect square on the left side: (v + 1)(v + 1) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (v + 1) equal to 6.782329983 and -6.782329983.Subproblem 1
v + 1 = 6.782329983 Simplifying v + 1 = 6.782329983 Reorder the terms: 1 + v = 6.782329983 Solving 1 + v = 6.782329983 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + v = 6.782329983 + -1 Combine like terms: 1 + -1 = 0 0 + v = 6.782329983 + -1 v = 6.782329983 + -1 Combine like terms: 6.782329983 + -1 = 5.782329983 v = 5.782329983 Simplifying v = 5.782329983Subproblem 2
v + 1 = -6.782329983 Simplifying v + 1 = -6.782329983 Reorder the terms: 1 + v = -6.782329983 Solving 1 + v = -6.782329983 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + v = -6.782329983 + -1 Combine like terms: 1 + -1 = 0 0 + v = -6.782329983 + -1 v = -6.782329983 + -1 Combine like terms: -6.782329983 + -1 = -7.782329983 v = -7.782329983 Simplifying v = -7.782329983Solution
The solution to the problem is based on the solutions from the subproblems. v = {5.782329983, -7.782329983}
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