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Simplifying v2 + 16v + -37 = 0 Reorder the terms: -37 + 16v + v2 = 0 Solving -37 + 16v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + 16v + 37 + v2 = 0 + 37 Reorder the terms: -37 + 37 + 16v + v2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + 16v + v2 = 0 + 37 16v + v2 = 0 + 37 Combine like terms: 0 + 37 = 37 16v + v2 = 37 The v term is 16v. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16v + 64 + v2 = 37 + 64 Reorder the terms: 64 + 16v + v2 = 37 + 64 Combine like terms: 37 + 64 = 101 64 + 16v + v2 = 101 Factor a perfect square on the left side: (v + 8)(v + 8) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (v + 8) equal to 10.049875621 and -10.049875621.Subproblem 1
v + 8 = 10.049875621 Simplifying v + 8 = 10.049875621 Reorder the terms: 8 + v = 10.049875621 Solving 8 + v = 10.049875621 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + v = 10.049875621 + -8 Combine like terms: 8 + -8 = 0 0 + v = 10.049875621 + -8 v = 10.049875621 + -8 Combine like terms: 10.049875621 + -8 = 2.049875621 v = 2.049875621 Simplifying v = 2.049875621Subproblem 2
v + 8 = -10.049875621 Simplifying v + 8 = -10.049875621 Reorder the terms: 8 + v = -10.049875621 Solving 8 + v = -10.049875621 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + v = -10.049875621 + -8 Combine like terms: 8 + -8 = 0 0 + v = -10.049875621 + -8 v = -10.049875621 + -8 Combine like terms: -10.049875621 + -8 = -18.049875621 v = -18.049875621 Simplifying v = -18.049875621Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.049875621, -18.049875621}
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