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Simplifying v2 + -40v + 40 = 0 Reorder the terms: 40 + -40v + v2 = 0 Solving 40 + -40v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + -40v + -40 + v2 = 0 + -40 Reorder the terms: 40 + -40 + -40v + v2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -40v + v2 = 0 + -40 -40v + v2 = 0 + -40 Combine like terms: 0 + -40 = -40 -40v + v2 = -40 The v term is -40v. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40v + 400 + v2 = -40 + 400 Reorder the terms: 400 + -40v + v2 = -40 + 400 Combine like terms: -40 + 400 = 360 400 + -40v + v2 = 360 Factor a perfect square on the left side: (v + -20)(v + -20) = 360 Calculate the square root of the right side: 18.973665961 Break this problem into two subproblems by setting (v + -20) equal to 18.973665961 and -18.973665961.Subproblem 1
v + -20 = 18.973665961 Simplifying v + -20 = 18.973665961 Reorder the terms: -20 + v = 18.973665961 Solving -20 + v = 18.973665961 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + v = 18.973665961 + 20 Combine like terms: -20 + 20 = 0 0 + v = 18.973665961 + 20 v = 18.973665961 + 20 Combine like terms: 18.973665961 + 20 = 38.973665961 v = 38.973665961 Simplifying v = 38.973665961Subproblem 2
v + -20 = -18.973665961 Simplifying v + -20 = -18.973665961 Reorder the terms: -20 + v = -18.973665961 Solving -20 + v = -18.973665961 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + v = -18.973665961 + 20 Combine like terms: -20 + 20 = 0 0 + v = -18.973665961 + 20 v = -18.973665961 + 20 Combine like terms: -18.973665961 + 20 = 1.026334039 v = 1.026334039 Simplifying v = 1.026334039Solution
The solution to the problem is based on the solutions from the subproblems. v = {38.973665961, 1.026334039}
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