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Simplifying v2 + 3v + -42 = 0 Reorder the terms: -42 + 3v + v2 = 0 Solving -42 + 3v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + 3v + 42 + v2 = 0 + 42 Reorder the terms: -42 + 42 + 3v + v2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 3v + v2 = 0 + 42 3v + v2 = 0 + 42 Combine like terms: 0 + 42 = 42 3v + v2 = 42 The v term is 3v. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3v + 2.25 + v2 = 42 + 2.25 Reorder the terms: 2.25 + 3v + v2 = 42 + 2.25 Combine like terms: 42 + 2.25 = 44.25 2.25 + 3v + v2 = 44.25 Factor a perfect square on the left side: (v + 1.5)(v + 1.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (v + 1.5) equal to 6.652067348 and -6.652067348.Subproblem 1
v + 1.5 = 6.652067348 Simplifying v + 1.5 = 6.652067348 Reorder the terms: 1.5 + v = 6.652067348 Solving 1.5 + v = 6.652067348 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + v = 6.652067348 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + v = 6.652067348 + -1.5 v = 6.652067348 + -1.5 Combine like terms: 6.652067348 + -1.5 = 5.152067348 v = 5.152067348 Simplifying v = 5.152067348Subproblem 2
v + 1.5 = -6.652067348 Simplifying v + 1.5 = -6.652067348 Reorder the terms: 1.5 + v = -6.652067348 Solving 1.5 + v = -6.652067348 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + v = -6.652067348 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + v = -6.652067348 + -1.5 v = -6.652067348 + -1.5 Combine like terms: -6.652067348 + -1.5 = -8.152067348 v = -8.152067348 Simplifying v = -8.152067348Solution
The solution to the problem is based on the solutions from the subproblems. v = {5.152067348, -8.152067348}
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