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Simplifying v2 + 8v = 1 Reorder the terms: 8v + v2 = 1 Solving 8v + v2 = 1 Solving for variable 'v'. Reorder the terms: -1 + 8v + v2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 8v + v2 = 0 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 = 0.123105626 v = 0.123105626 Simplifying v = 0.123105626Subproblem 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 = -8.123105626 v = -8.123105626 Simplifying v = -8.123105626Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.123105626, -8.123105626}
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