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Simplifying 8v2 + -9v + -1 = 0 Reorder the terms: -1 + -9v + 8v2 = 0 Solving -1 + -9v + 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 + -1.125v + v2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -1.125v + 0.125 + v2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -1.125v + v2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -1.125v + v2 = 0 + 0.125 -1.125v + v2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -1.125v + v2 = 0.125 The v term is -1.125v. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125v + 0.31640625 + v2 = 0.125 + 0.31640625 Reorder the terms: 0.31640625 + -1.125v + v2 = 0.125 + 0.31640625 Combine like terms: 0.125 + 0.31640625 = 0.44140625 0.31640625 + -1.125v + v2 = 0.44140625 Factor a perfect square on the left side: (v + -0.5625)(v + -0.5625) = 0.44140625 Calculate the square root of the right side: 0.664384113 Break this problem into two subproblems by setting (v + -0.5625) equal to 0.664384113 and -0.664384113.Subproblem 1
v + -0.5625 = 0.664384113 Simplifying v + -0.5625 = 0.664384113 Reorder the terms: -0.5625 + v = 0.664384113 Solving -0.5625 + v = 0.664384113 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + v = 0.664384113 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + v = 0.664384113 + 0.5625 v = 0.664384113 + 0.5625 Combine like terms: 0.664384113 + 0.5625 = 1.226884113 v = 1.226884113 Simplifying v = 1.226884113Subproblem 2
v + -0.5625 = -0.664384113 Simplifying v + -0.5625 = -0.664384113 Reorder the terms: -0.5625 + v = -0.664384113 Solving -0.5625 + v = -0.664384113 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + v = -0.664384113 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + v = -0.664384113 + 0.5625 v = -0.664384113 + 0.5625 Combine like terms: -0.664384113 + 0.5625 = -0.101884113 v = -0.101884113 Simplifying v = -0.101884113Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.226884113, -0.101884113}
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