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Simplifying 8v2 + -3v + -61 = 0 Reorder the terms: -61 + -3v + 8v2 = 0 Solving -61 + -3v + 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'. -7.625 + -0.375v + v2 = 0 Move the constant term to the right: Add '7.625' to each side of the equation. -7.625 + -0.375v + 7.625 + v2 = 0 + 7.625 Reorder the terms: -7.625 + 7.625 + -0.375v + v2 = 0 + 7.625 Combine like terms: -7.625 + 7.625 = 0.000 0.000 + -0.375v + v2 = 0 + 7.625 -0.375v + v2 = 0 + 7.625 Combine like terms: 0 + 7.625 = 7.625 -0.375v + v2 = 7.625 The v term is -0.375v. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375v + 0.03515625 + v2 = 7.625 + 0.03515625 Reorder the terms: 0.03515625 + -0.375v + v2 = 7.625 + 0.03515625 Combine like terms: 7.625 + 0.03515625 = 7.66015625 0.03515625 + -0.375v + v2 = 7.66015625 Factor a perfect square on the left side: (v + -0.1875)(v + -0.1875) = 7.66015625 Calculate the square root of the right side: 2.767698728 Break this problem into two subproblems by setting (v + -0.1875) equal to 2.767698728 and -2.767698728.Subproblem 1
v + -0.1875 = 2.767698728 Simplifying v + -0.1875 = 2.767698728 Reorder the terms: -0.1875 + v = 2.767698728 Solving -0.1875 + v = 2.767698728 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + v = 2.767698728 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + v = 2.767698728 + 0.1875 v = 2.767698728 + 0.1875 Combine like terms: 2.767698728 + 0.1875 = 2.955198728 v = 2.955198728 Simplifying v = 2.955198728Subproblem 2
v + -0.1875 = -2.767698728 Simplifying v + -0.1875 = -2.767698728 Reorder the terms: -0.1875 + v = -2.767698728 Solving -0.1875 + v = -2.767698728 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + v = -2.767698728 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + v = -2.767698728 + 0.1875 v = -2.767698728 + 0.1875 Combine like terms: -2.767698728 + 0.1875 = -2.580198728 v = -2.580198728 Simplifying v = -2.580198728Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.955198728, -2.580198728}
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