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Simplifying v2 + 8v + -16 = 0 Reorder the terms: -16 + 8v + v2 = 0 Solving -16 + 8v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 8v + 16 + v2 = 0 + 16 Reorder the terms: -16 + 16 + 8v + v2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 8v + v2 = 0 + 16 8v + v2 = 0 + 16 Combine like terms: 0 + 16 = 16 8v + v2 = 16 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 = 16 + 16 Reorder the terms: 16 + 8v + v2 = 16 + 16 Combine like terms: 16 + 16 = 32 16 + 8v + v2 = 32 Factor a perfect square on the left side: (v + 4)(v + 4) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (v + 4) equal to 5.656854249 and -5.656854249.Subproblem 1
v + 4 = 5.656854249 Simplifying v + 4 = 5.656854249 Reorder the terms: 4 + v = 5.656854249 Solving 4 + v = 5.656854249 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 = 5.656854249 + -4 Combine like terms: 4 + -4 = 0 0 + v = 5.656854249 + -4 v = 5.656854249 + -4 Combine like terms: 5.656854249 + -4 = 1.656854249 v = 1.656854249 Simplifying v = 1.656854249Subproblem 2
v + 4 = -5.656854249 Simplifying v + 4 = -5.656854249 Reorder the terms: 4 + v = -5.656854249 Solving 4 + v = -5.656854249 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 = -5.656854249 + -4 Combine like terms: 4 + -4 = 0 0 + v = -5.656854249 + -4 v = -5.656854249 + -4 Combine like terms: -5.656854249 + -4 = -9.656854249 v = -9.656854249 Simplifying v = -9.656854249Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.656854249, -9.656854249}
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