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Simplifying v2 = 8v + 2 Reorder the terms: v2 = 2 + 8v Solving v2 = 2 + 8v Solving for variable 'v'. Reorder the terms: -2 + -8v + v2 = 2 + 8v + -2 + -8v Reorder the terms: -2 + -8v + v2 = 2 + -2 + 8v + -8v Combine like terms: 2 + -2 = 0 -2 + -8v + v2 = 0 + 8v + -8v -2 + -8v + v2 = 8v + -8v Combine like terms: 8v + -8v = 0 -2 + -8v + v2 = 0 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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