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Simplifying 16v2 + 2v + -15 = 0 Reorder the terms: -15 + 2v + 16v2 = 0 Solving -15 + 2v + 16v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.9375 + 0.125v + v2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + 0.125v + 0.9375 + v2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + 0.125v + v2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + 0.125v + v2 = 0 + 0.9375 0.125v + v2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 0.125v + v2 = 0.9375 The v term is 0.125v. Take half its coefficient (0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. 0.125v + 0.00390625 + v2 = 0.9375 + 0.00390625 Reorder the terms: 0.00390625 + 0.125v + v2 = 0.9375 + 0.00390625 Combine like terms: 0.9375 + 0.00390625 = 0.94140625 0.00390625 + 0.125v + v2 = 0.94140625 Factor a perfect square on the left side: (v + 0.0625)(v + 0.0625) = 0.94140625 Calculate the square root of the right side: 0.970260919 Break this problem into two subproblems by setting (v + 0.0625) equal to 0.970260919 and -0.970260919.Subproblem 1
v + 0.0625 = 0.970260919 Simplifying v + 0.0625 = 0.970260919 Reorder the terms: 0.0625 + v = 0.970260919 Solving 0.0625 + v = 0.970260919 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + v = 0.970260919 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + v = 0.970260919 + -0.0625 v = 0.970260919 + -0.0625 Combine like terms: 0.970260919 + -0.0625 = 0.907760919 v = 0.907760919 Simplifying v = 0.907760919Subproblem 2
v + 0.0625 = -0.970260919 Simplifying v + 0.0625 = -0.970260919 Reorder the terms: 0.0625 + v = -0.970260919 Solving 0.0625 + v = -0.970260919 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + v = -0.970260919 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + v = -0.970260919 + -0.0625 v = -0.970260919 + -0.0625 Combine like terms: -0.970260919 + -0.0625 = -1.032760919 v = -1.032760919 Simplifying v = -1.032760919Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.907760919, -1.032760919}
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