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Simplifying v2 + 4v + -31 = 0 Reorder the terms: -31 + 4v + v2 = 0 Solving -31 + 4v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + 4v + 31 + v2 = 0 + 31 Reorder the terms: -31 + 31 + 4v + v2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 4v + v2 = 0 + 31 4v + v2 = 0 + 31 Combine like terms: 0 + 31 = 31 4v + v2 = 31 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 = 31 + 4 Reorder the terms: 4 + 4v + v2 = 31 + 4 Combine like terms: 31 + 4 = 35 4 + 4v + v2 = 35 Factor a perfect square on the left side: (v + 2)(v + 2) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (v + 2) equal to 5.916079783 and -5.916079783.Subproblem 1
v + 2 = 5.916079783 Simplifying v + 2 = 5.916079783 Reorder the terms: 2 + v = 5.916079783 Solving 2 + v = 5.916079783 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 = 5.916079783 + -2 Combine like terms: 2 + -2 = 0 0 + v = 5.916079783 + -2 v = 5.916079783 + -2 Combine like terms: 5.916079783 + -2 = 3.916079783 v = 3.916079783 Simplifying v = 3.916079783Subproblem 2
v + 2 = -5.916079783 Simplifying v + 2 = -5.916079783 Reorder the terms: 2 + v = -5.916079783 Solving 2 + v = -5.916079783 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 = -5.916079783 + -2 Combine like terms: 2 + -2 = 0 0 + v = -5.916079783 + -2 v = -5.916079783 + -2 Combine like terms: -5.916079783 + -2 = -7.916079783 v = -7.916079783 Simplifying v = -7.916079783Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.916079783, -7.916079783}
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