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Simplifying 8v2 + -10v + -1 = 0 Reorder the terms: -1 + -10v + 8v2 = 0 Solving -1 + -10v + 8v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + -1.25v + v2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -1.25v + 0.125 + v2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -1.25v + v2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -1.25v + v2 = 0 + 0.125 -1.25v + v2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -1.25v + v2 = 0.125 The v term is -1.25v. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25v + 0.390625 + v2 = 0.125 + 0.390625 Reorder the terms: 0.390625 + -1.25v + v2 = 0.125 + 0.390625 Combine like terms: 0.125 + 0.390625 = 0.515625 0.390625 + -1.25v + v2 = 0.515625 Factor a perfect square on the left side: (v + -0.625)(v + -0.625) = 0.515625 Calculate the square root of the right side: 0.718070331 Break this problem into two subproblems by setting (v + -0.625) equal to 0.718070331 and -0.718070331.Subproblem 1
v + -0.625 = 0.718070331 Simplifying v + -0.625 = 0.718070331 Reorder the terms: -0.625 + v = 0.718070331 Solving -0.625 + v = 0.718070331 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + v = 0.718070331 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + v = 0.718070331 + 0.625 v = 0.718070331 + 0.625 Combine like terms: 0.718070331 + 0.625 = 1.343070331 v = 1.343070331 Simplifying v = 1.343070331Subproblem 2
v + -0.625 = -0.718070331 Simplifying v + -0.625 = -0.718070331 Reorder the terms: -0.625 + v = -0.718070331 Solving -0.625 + v = -0.718070331 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + v = -0.718070331 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + v = -0.718070331 + 0.625 v = -0.718070331 + 0.625 Combine like terms: -0.718070331 + 0.625 = -0.093070331 v = -0.093070331 Simplifying v = -0.093070331Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.343070331, -0.093070331}
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