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Simplifying v2 + 13v + 35 = 0 Reorder the terms: 35 + 13v + v2 = 0 Solving 35 + 13v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + 13v + -35 + v2 = 0 + -35 Reorder the terms: 35 + -35 + 13v + v2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 13v + v2 = 0 + -35 13v + v2 = 0 + -35 Combine like terms: 0 + -35 = -35 13v + v2 = -35 The v term is 13v. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13v + 42.25 + v2 = -35 + 42.25 Reorder the terms: 42.25 + 13v + v2 = -35 + 42.25 Combine like terms: -35 + 42.25 = 7.25 42.25 + 13v + v2 = 7.25 Factor a perfect square on the left side: (v + 6.5)(v + 6.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (v + 6.5) equal to 2.692582404 and -2.692582404.Subproblem 1
v + 6.5 = 2.692582404 Simplifying v + 6.5 = 2.692582404 Reorder the terms: 6.5 + v = 2.692582404 Solving 6.5 + v = 2.692582404 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + v = 2.692582404 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + v = 2.692582404 + -6.5 v = 2.692582404 + -6.5 Combine like terms: 2.692582404 + -6.5 = -3.807417596 v = -3.807417596 Simplifying v = -3.807417596Subproblem 2
v + 6.5 = -2.692582404 Simplifying v + 6.5 = -2.692582404 Reorder the terms: 6.5 + v = -2.692582404 Solving 6.5 + v = -2.692582404 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + v = -2.692582404 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + v = -2.692582404 + -6.5 v = -2.692582404 + -6.5 Combine like terms: -2.692582404 + -6.5 = -9.192582404 v = -9.192582404 Simplifying v = -9.192582404Solution
The solution to the problem is based on the solutions from the subproblems. v = {-3.807417596, -9.192582404}
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