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Simplifying v2 + -4v + -15 = 0 Reorder the terms: -15 + -4v + v2 = 0 Solving -15 + -4v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -4v + 15 + v2 = 0 + 15 Reorder the terms: -15 + 15 + -4v + v2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -4v + v2 = 0 + 15 -4v + v2 = 0 + 15 Combine like terms: 0 + 15 = 15 -4v + v2 = 15 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 = 15 + 4 Reorder the terms: 4 + -4v + v2 = 15 + 4 Combine like terms: 15 + 4 = 19 4 + -4v + v2 = 19 Factor a perfect square on the left side: (v + -2)(v + -2) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (v + -2) equal to 4.358898944 and -4.358898944.Subproblem 1
v + -2 = 4.358898944 Simplifying v + -2 = 4.358898944 Reorder the terms: -2 + v = 4.358898944 Solving -2 + v = 4.358898944 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 = 4.358898944 + 2 Combine like terms: -2 + 2 = 0 0 + v = 4.358898944 + 2 v = 4.358898944 + 2 Combine like terms: 4.358898944 + 2 = 6.358898944 v = 6.358898944 Simplifying v = 6.358898944Subproblem 2
v + -2 = -4.358898944 Simplifying v + -2 = -4.358898944 Reorder the terms: -2 + v = -4.358898944 Solving -2 + v = -4.358898944 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 = -4.358898944 + 2 Combine like terms: -2 + 2 = 0 0 + v = -4.358898944 + 2 v = -4.358898944 + 2 Combine like terms: -4.358898944 + 2 = -2.358898944 v = -2.358898944 Simplifying v = -2.358898944Solution
The solution to the problem is based on the solutions from the subproblems. v = {6.358898944, -2.358898944}
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