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Simplifying v2 + 8v + 2 = 0 Reorder the terms: 2 + 8v + v2 = 0 Solving 2 + 8v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 8v + -2 + v2 = 0 + -2 Reorder the terms: 2 + -2 + 8v + v2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 8v + v2 = 0 + -2 8v + v2 = 0 + -2 Combine like terms: 0 + -2 = -2 8v + v2 = -2 The v term is 8v. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8v + 16 + v2 = -2 + 16 Reorder the terms: 16 + 8v + v2 = -2 + 16 Combine like terms: -2 + 16 = 14 16 + 8v + v2 = 14 Factor a perfect square on the left side: (v + 4)(v + 4) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (v + 4) equal to 3.741657387 and -3.741657387.Subproblem 1
v + 4 = 3.741657387 Simplifying v + 4 = 3.741657387 Reorder the terms: 4 + v = 3.741657387 Solving 4 + v = 3.741657387 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + v = 3.741657387 + -4 Combine like terms: 4 + -4 = 0 0 + v = 3.741657387 + -4 v = 3.741657387 + -4 Combine like terms: 3.741657387 + -4 = -0.258342613 v = -0.258342613 Simplifying v = -0.258342613Subproblem 2
v + 4 = -3.741657387 Simplifying v + 4 = -3.741657387 Reorder the terms: 4 + v = -3.741657387 Solving 4 + v = -3.741657387 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + v = -3.741657387 + -4 Combine like terms: 4 + -4 = 0 0 + v = -3.741657387 + -4 v = -3.741657387 + -4 Combine like terms: -3.741657387 + -4 = -7.741657387 v = -7.741657387 Simplifying v = -7.741657387Solution
The solution to the problem is based on the solutions from the subproblems. v = {-0.258342613, -7.741657387}
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