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Simplifying v2 + -4v + -37 = 2 Reorder the terms: -37 + -4v + v2 = 2 Solving -37 + -4v + v2 = 2 Solving for variable 'v'. Reorder the terms: -37 + -2 + -4v + v2 = 2 + -2 Combine like terms: -37 + -2 = -39 -39 + -4v + v2 = 2 + -2 Combine like terms: 2 + -2 = 0 -39 + -4v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + -4v + 39 + v2 = 0 + 39 Reorder the terms: -39 + 39 + -4v + v2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -4v + v2 = 0 + 39 -4v + v2 = 0 + 39 Combine like terms: 0 + 39 = 39 -4v + v2 = 39 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 = 39 + 4 Reorder the terms: 4 + -4v + v2 = 39 + 4 Combine like terms: 39 + 4 = 43 4 + -4v + v2 = 43 Factor a perfect square on the left side: (v + -2)(v + -2) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (v + -2) equal to 6.557438524 and -6.557438524.Subproblem 1
v + -2 = 6.557438524 Simplifying v + -2 = 6.557438524 Reorder the terms: -2 + v = 6.557438524 Solving -2 + v = 6.557438524 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 = 6.557438524 + 2 Combine like terms: -2 + 2 = 0 0 + v = 6.557438524 + 2 v = 6.557438524 + 2 Combine like terms: 6.557438524 + 2 = 8.557438524 v = 8.557438524 Simplifying v = 8.557438524Subproblem 2
v + -2 = -6.557438524 Simplifying v + -2 = -6.557438524 Reorder the terms: -2 + v = -6.557438524 Solving -2 + v = -6.557438524 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 = -6.557438524 + 2 Combine like terms: -2 + 2 = 0 0 + v = -6.557438524 + 2 v = -6.557438524 + 2 Combine like terms: -6.557438524 + 2 = -4.557438524 v = -4.557438524 Simplifying v = -4.557438524Solution
The solution to the problem is based on the solutions from the subproblems. v = {8.557438524, -4.557438524}
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