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Simplifying v2 = 13v + 3 Reorder the terms: v2 = 3 + 13v Solving v2 = 3 + 13v Solving for variable 'v'. Reorder the terms: -3 + -13v + v2 = 3 + 13v + -3 + -13v Reorder the terms: -3 + -13v + v2 = 3 + -3 + 13v + -13v Combine like terms: 3 + -3 = 0 -3 + -13v + v2 = 0 + 13v + -13v -3 + -13v + v2 = 13v + -13v Combine like terms: 13v + -13v = 0 -3 + -13v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -13v + 3 + v2 = 0 + 3 Reorder the terms: -3 + 3 + -13v + v2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -13v + v2 = 0 + 3 -13v + v2 = 0 + 3 Combine like terms: 0 + 3 = 3 -13v + v2 = 3 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 = 3 + 42.25 Reorder the terms: 42.25 + -13v + v2 = 3 + 42.25 Combine like terms: 3 + 42.25 = 45.25 42.25 + -13v + v2 = 45.25 Factor a perfect square on the left side: (v + -6.5)(v + -6.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (v + -6.5) equal to 6.726812024 and -6.726812024.Subproblem 1
v + -6.5 = 6.726812024 Simplifying v + -6.5 = 6.726812024 Reorder the terms: -6.5 + v = 6.726812024 Solving -6.5 + v = 6.726812024 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 = 6.726812024 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + v = 6.726812024 + 6.5 v = 6.726812024 + 6.5 Combine like terms: 6.726812024 + 6.5 = 13.226812024 v = 13.226812024 Simplifying v = 13.226812024Subproblem 2
v + -6.5 = -6.726812024 Simplifying v + -6.5 = -6.726812024 Reorder the terms: -6.5 + v = -6.726812024 Solving -6.5 + v = -6.726812024 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 = -6.726812024 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + v = -6.726812024 + 6.5 v = -6.726812024 + 6.5 Combine like terms: -6.726812024 + 6.5 = -0.226812024 v = -0.226812024 Simplifying v = -0.226812024Solution
The solution to the problem is based on the solutions from the subproblems. v = {13.226812024, -0.226812024}
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