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Simplifying v2 + 15v = -15 Reorder the terms: 15v + v2 = -15 Solving 15v + v2 = -15 Solving for variable 'v'. Reorder the terms: 15 + 15v + v2 = -15 + 15 Combine like terms: -15 + 15 = 0 15 + 15v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 15v + -15 + v2 = 0 + -15 Reorder the terms: 15 + -15 + 15v + v2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 15v + v2 = 0 + -15 15v + v2 = 0 + -15 Combine like terms: 0 + -15 = -15 15v + v2 = -15 The v term is 15v. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15v + 56.25 + v2 = -15 + 56.25 Reorder the terms: 56.25 + 15v + v2 = -15 + 56.25 Combine like terms: -15 + 56.25 = 41.25 56.25 + 15v + v2 = 41.25 Factor a perfect square on the left side: (v + 7.5)(v + 7.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (v + 7.5) equal to 6.422616289 and -6.422616289.Subproblem 1
v + 7.5 = 6.422616289 Simplifying v + 7.5 = 6.422616289 Reorder the terms: 7.5 + v = 6.422616289 Solving 7.5 + v = 6.422616289 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + v = 6.422616289 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + v = 6.422616289 + -7.5 v = 6.422616289 + -7.5 Combine like terms: 6.422616289 + -7.5 = -1.077383711 v = -1.077383711 Simplifying v = -1.077383711Subproblem 2
v + 7.5 = -6.422616289 Simplifying v + 7.5 = -6.422616289 Reorder the terms: 7.5 + v = -6.422616289 Solving 7.5 + v = -6.422616289 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + v = -6.422616289 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + v = -6.422616289 + -7.5 v = -6.422616289 + -7.5 Combine like terms: -6.422616289 + -7.5 = -13.922616289 v = -13.922616289 Simplifying v = -13.922616289Solution
The solution to the problem is based on the solutions from the subproblems. v = {-1.077383711, -13.922616289}
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