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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 = 18 16 + -8V + V2 = 18 Factor a perfect square on the left side: (V + -4)(V + -4) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (V + -4) equal to 4.242640687 and -4.242640687.Subproblem 1
V + -4 = 4.242640687 Simplifying V + -4 = 4.242640687 Reorder the terms: -4 + V = 4.242640687 Solving -4 + V = 4.242640687 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 = 4.242640687 + 4 Combine like terms: -4 + 4 = 0 0 + V = 4.242640687 + 4 V = 4.242640687 + 4 Combine like terms: 4.242640687 + 4 = 8.242640687 V = 8.242640687 Simplifying V = 8.242640687Subproblem 2
V + -4 = -4.242640687 Simplifying V + -4 = -4.242640687 Reorder the terms: -4 + V = -4.242640687 Solving -4 + V = -4.242640687 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 = -4.242640687 + 4 Combine like terms: -4 + 4 = 0 0 + V = -4.242640687 + 4 V = -4.242640687 + 4 Combine like terms: -4.242640687 + 4 = -0.242640687 V = -0.242640687 Simplifying V = -0.242640687Solution
The solution to the problem is based on the solutions from the subproblems. V = {8.242640687, -0.242640687}
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