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Simplifying v2 + -8v + -1 = 0 Reorder the terms: -1 + -8v + v2 = 0 Solving -1 + -8v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -8v + 1 + v2 = 0 + 1 Reorder the terms: -1 + 1 + -8v + v2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -8v + v2 = 0 + 1 -8v + v2 = 0 + 1 Combine like terms: 0 + 1 = 1 -8v + v2 = 1 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 = 1 + 16 Reorder the terms: 16 + -8v + v2 = 1 + 16 Combine like terms: 1 + 16 = 17 16 + -8v + v2 = 17 Factor a perfect square on the left side: (v + -4)(v + -4) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (v + -4) equal to 4.123105626 and -4.123105626.Subproblem 1
v + -4 = 4.123105626 Simplifying v + -4 = 4.123105626 Reorder the terms: -4 + v = 4.123105626 Solving -4 + v = 4.123105626 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 = 4.123105626 + 4 Combine like terms: -4 + 4 = 0 0 + v = 4.123105626 + 4 v = 4.123105626 + 4 Combine like terms: 4.123105626 + 4 = 8.123105626 v = 8.123105626 Simplifying v = 8.123105626Subproblem 2
v + -4 = -4.123105626 Simplifying v + -4 = -4.123105626 Reorder the terms: -4 + v = -4.123105626 Solving -4 + v = -4.123105626 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 = -4.123105626 + 4 Combine like terms: -4 + 4 = 0 0 + v = -4.123105626 + 4 v = -4.123105626 + 4 Combine like terms: -4.123105626 + 4 = -0.123105626 v = -0.123105626 Simplifying v = -0.123105626Solution
The solution to the problem is based on the solutions from the subproblems. v = {8.123105626, -0.123105626}
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