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Simplifying v2 + 2v + -25 = 0 Reorder the terms: -25 + 2v + v2 = 0 Solving -25 + 2v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 2v + 25 + v2 = 0 + 25 Reorder the terms: -25 + 25 + 2v + v2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 2v + v2 = 0 + 25 2v + v2 = 0 + 25 Combine like terms: 0 + 25 = 25 2v + v2 = 25 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 = 25 + 1 Reorder the terms: 1 + 2v + v2 = 25 + 1 Combine like terms: 25 + 1 = 26 1 + 2v + v2 = 26 Factor a perfect square on the left side: (v + 1)(v + 1) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (v + 1) equal to 5.099019514 and -5.099019514.Subproblem 1
v + 1 = 5.099019514 Simplifying v + 1 = 5.099019514 Reorder the terms: 1 + v = 5.099019514 Solving 1 + v = 5.099019514 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 = 5.099019514 + -1 Combine like terms: 1 + -1 = 0 0 + v = 5.099019514 + -1 v = 5.099019514 + -1 Combine like terms: 5.099019514 + -1 = 4.099019514 v = 4.099019514 Simplifying v = 4.099019514Subproblem 2
v + 1 = -5.099019514 Simplifying v + 1 = -5.099019514 Reorder the terms: 1 + v = -5.099019514 Solving 1 + v = -5.099019514 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 = -5.099019514 + -1 Combine like terms: 1 + -1 = 0 0 + v = -5.099019514 + -1 v = -5.099019514 + -1 Combine like terms: -5.099019514 + -1 = -6.099019514 v = -6.099019514 Simplifying v = -6.099019514Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.099019514, -6.099019514}
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