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Simplifying v2 + -5v = 38 Reorder the terms: -5v + v2 = 38 Solving -5v + v2 = 38 Solving for variable 'v'. Reorder the terms: -38 + -5v + v2 = 38 + -38 Combine like terms: 38 + -38 = 0 -38 + -5v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + -5v + 38 + v2 = 0 + 38 Reorder the terms: -38 + 38 + -5v + v2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + -5v + v2 = 0 + 38 -5v + v2 = 0 + 38 Combine like terms: 0 + 38 = 38 -5v + v2 = 38 The v term is -5v. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5v + 6.25 + v2 = 38 + 6.25 Reorder the terms: 6.25 + -5v + v2 = 38 + 6.25 Combine like terms: 38 + 6.25 = 44.25 6.25 + -5v + v2 = 44.25 Factor a perfect square on the left side: (v + -2.5)(v + -2.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (v + -2.5) equal to 6.652067348 and -6.652067348.Subproblem 1
v + -2.5 = 6.652067348 Simplifying v + -2.5 = 6.652067348 Reorder the terms: -2.5 + v = 6.652067348 Solving -2.5 + v = 6.652067348 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + v = 6.652067348 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + v = 6.652067348 + 2.5 v = 6.652067348 + 2.5 Combine like terms: 6.652067348 + 2.5 = 9.152067348 v = 9.152067348 Simplifying v = 9.152067348Subproblem 2
v + -2.5 = -6.652067348 Simplifying v + -2.5 = -6.652067348 Reorder the terms: -2.5 + v = -6.652067348 Solving -2.5 + v = -6.652067348 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + v = -6.652067348 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + v = -6.652067348 + 2.5 v = -6.652067348 + 2.5 Combine like terms: -6.652067348 + 2.5 = -4.152067348 v = -4.152067348 Simplifying v = -4.152067348Solution
The solution to the problem is based on the solutions from the subproblems. v = {9.152067348, -4.152067348}
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