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Simplifying v2 + -4v + -25 = 0 Reorder the terms: -25 + -4v + v2 = 0 Solving -25 + -4v + 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 + -4v + 25 + v2 = 0 + 25 Reorder the terms: -25 + 25 + -4v + v2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -4v + v2 = 0 + 25 -4v + v2 = 0 + 25 Combine like terms: 0 + 25 = 25 -4v + v2 = 25 The v term is -4v. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4v + 4 + v2 = 25 + 4 Reorder the terms: 4 + -4v + v2 = 25 + 4 Combine like terms: 25 + 4 = 29 4 + -4v + v2 = 29 Factor a perfect square on the left side: (v + -2)(v + -2) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (v + -2) equal to 5.385164807 and -5.385164807.Subproblem 1
v + -2 = 5.385164807 Simplifying v + -2 = 5.385164807 Reorder the terms: -2 + v = 5.385164807 Solving -2 + v = 5.385164807 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + v = 5.385164807 + 2 Combine like terms: -2 + 2 = 0 0 + v = 5.385164807 + 2 v = 5.385164807 + 2 Combine like terms: 5.385164807 + 2 = 7.385164807 v = 7.385164807 Simplifying v = 7.385164807Subproblem 2
v + -2 = -5.385164807 Simplifying v + -2 = -5.385164807 Reorder the terms: -2 + v = -5.385164807 Solving -2 + v = -5.385164807 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + v = -5.385164807 + 2 Combine like terms: -2 + 2 = 0 0 + v = -5.385164807 + 2 v = -5.385164807 + 2 Combine like terms: -5.385164807 + 2 = -3.385164807 v = -3.385164807 Simplifying v = -3.385164807Solution
The solution to the problem is based on the solutions from the subproblems. v = {7.385164807, -3.385164807}
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