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Simplifying v2 + 4v + -10 = 0 Reorder the terms: -10 + 4v + v2 = 0 Solving -10 + 4v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 4v + 10 + v2 = 0 + 10 Reorder the terms: -10 + 10 + 4v + v2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 4v + v2 = 0 + 10 4v + v2 = 0 + 10 Combine like terms: 0 + 10 = 10 4v + v2 = 10 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 = 10 + 4 Reorder the terms: 4 + 4v + v2 = 10 + 4 Combine like terms: 10 + 4 = 14 4 + 4v + v2 = 14 Factor a perfect square on the left side: (v + 2)(v + 2) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (v + 2) equal to 3.741657387 and -3.741657387.Subproblem 1
v + 2 = 3.741657387 Simplifying v + 2 = 3.741657387 Reorder the terms: 2 + v = 3.741657387 Solving 2 + v = 3.741657387 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 = 3.741657387 + -2 Combine like terms: 2 + -2 = 0 0 + v = 3.741657387 + -2 v = 3.741657387 + -2 Combine like terms: 3.741657387 + -2 = 1.741657387 v = 1.741657387 Simplifying v = 1.741657387Subproblem 2
v + 2 = -3.741657387 Simplifying v + 2 = -3.741657387 Reorder the terms: 2 + v = -3.741657387 Solving 2 + v = -3.741657387 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 = -3.741657387 + -2 Combine like terms: 2 + -2 = 0 0 + v = -3.741657387 + -2 v = -3.741657387 + -2 Combine like terms: -3.741657387 + -2 = -5.741657387 v = -5.741657387 Simplifying v = -5.741657387Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.741657387, -5.741657387}
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