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Simplifying v2 + -3v + -14 = 0 Reorder the terms: -14 + -3v + v2 = 0 Solving -14 + -3v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -3v + 14 + v2 = 0 + 14 Reorder the terms: -14 + 14 + -3v + v2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -3v + v2 = 0 + 14 -3v + v2 = 0 + 14 Combine like terms: 0 + 14 = 14 -3v + v2 = 14 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 = 14 + 2.25 Reorder the terms: 2.25 + -3v + v2 = 14 + 2.25 Combine like terms: 14 + 2.25 = 16.25 2.25 + -3v + v2 = 16.25 Factor a perfect square on the left side: (v + -1.5)(v + -1.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (v + -1.5) equal to 4.031128874 and -4.031128874.Subproblem 1
v + -1.5 = 4.031128874 Simplifying v + -1.5 = 4.031128874 Reorder the terms: -1.5 + v = 4.031128874 Solving -1.5 + v = 4.031128874 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 = 4.031128874 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + v = 4.031128874 + 1.5 v = 4.031128874 + 1.5 Combine like terms: 4.031128874 + 1.5 = 5.531128874 v = 5.531128874 Simplifying v = 5.531128874Subproblem 2
v + -1.5 = -4.031128874 Simplifying v + -1.5 = -4.031128874 Reorder the terms: -1.5 + v = -4.031128874 Solving -1.5 + v = -4.031128874 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 = -4.031128874 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + v = -4.031128874 + 1.5 v = -4.031128874 + 1.5 Combine like terms: -4.031128874 + 1.5 = -2.531128874 v = -2.531128874 Simplifying v = -2.531128874Solution
The solution to the problem is based on the solutions from the subproblems. v = {5.531128874, -2.531128874}
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