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Simplifying 6v2 + -9v + 1 = 0 Reorder the terms: 1 + -9v + 6v2 = 0 Solving 1 + -9v + 6v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.1666666667 + -1.5v + v2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + -1.5v + -0.1666666667 + v2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + -1.5v + v2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + -1.5v + v2 = 0 + -0.1666666667 -1.5v + v2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 -1.5v + v2 = -0.1666666667 The v term is -1.5v. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5v + 0.5625 + v2 = -0.1666666667 + 0.5625 Reorder the terms: 0.5625 + -1.5v + v2 = -0.1666666667 + 0.5625 Combine like terms: -0.1666666667 + 0.5625 = 0.3958333333 0.5625 + -1.5v + v2 = 0.3958333333 Factor a perfect square on the left side: (v + -0.75)(v + -0.75) = 0.3958333333 Calculate the square root of the right side: 0.62915287 Break this problem into two subproblems by setting (v + -0.75) equal to 0.62915287 and -0.62915287.Subproblem 1
v + -0.75 = 0.62915287 Simplifying v + -0.75 = 0.62915287 Reorder the terms: -0.75 + v = 0.62915287 Solving -0.75 + v = 0.62915287 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + v = 0.62915287 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + v = 0.62915287 + 0.75 v = 0.62915287 + 0.75 Combine like terms: 0.62915287 + 0.75 = 1.37915287 v = 1.37915287 Simplifying v = 1.37915287Subproblem 2
v + -0.75 = -0.62915287 Simplifying v + -0.75 = -0.62915287 Reorder the terms: -0.75 + v = -0.62915287 Solving -0.75 + v = -0.62915287 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + v = -0.62915287 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + v = -0.62915287 + 0.75 v = -0.62915287 + 0.75 Combine like terms: -0.62915287 + 0.75 = 0.12084713 v = 0.12084713 Simplifying v = 0.12084713Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.37915287, 0.12084713}
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