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Simplifying v2 + -4v = 37 Reorder the terms: -4v + v2 = 37 Solving -4v + v2 = 37 Solving for variable 'v'. Reorder the terms: -37 + -4v + v2 = 37 + -37 Combine like terms: 37 + -37 = 0 -37 + -4v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + -4v + 37 + v2 = 0 + 37 Reorder the terms: -37 + 37 + -4v + v2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -4v + v2 = 0 + 37 -4v + v2 = 0 + 37 Combine like terms: 0 + 37 = 37 -4v + v2 = 37 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 = 37 + 4 Reorder the terms: 4 + -4v + v2 = 37 + 4 Combine like terms: 37 + 4 = 41 4 + -4v + v2 = 41 Factor a perfect square on the left side: (v + -2)(v + -2) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (v + -2) equal to 6.403124237 and -6.403124237.Subproblem 1
v + -2 = 6.403124237 Simplifying v + -2 = 6.403124237 Reorder the terms: -2 + v = 6.403124237 Solving -2 + v = 6.403124237 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 = 6.403124237 + 2 Combine like terms: -2 + 2 = 0 0 + v = 6.403124237 + 2 v = 6.403124237 + 2 Combine like terms: 6.403124237 + 2 = 8.403124237 v = 8.403124237 Simplifying v = 8.403124237Subproblem 2
v + -2 = -6.403124237 Simplifying v + -2 = -6.403124237 Reorder the terms: -2 + v = -6.403124237 Solving -2 + v = -6.403124237 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 = -6.403124237 + 2 Combine like terms: -2 + 2 = 0 0 + v = -6.403124237 + 2 v = -6.403124237 + 2 Combine like terms: -6.403124237 + 2 = -4.403124237 v = -4.403124237 Simplifying v = -4.403124237Solution
The solution to the problem is based on the solutions from the subproblems. v = {8.403124237, -4.403124237}
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