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Simplifying 6v2 + -5 = -9v Reorder the terms: -5 + 6v2 = -9v Solving -5 + 6v2 = -9v Solving for variable 'v'. Reorder the terms: -5 + 9v + 6v2 = -9v + 9v Combine like terms: -9v + 9v = 0 -5 + 9v + 6v2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.8333333333 + 1.5v + v2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + 1.5v + 0.8333333333 + v2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + 1.5v + v2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + 1.5v + v2 = 0 + 0.8333333333 1.5v + v2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 1.5v + v2 = 0.8333333333 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 = 0.8333333333 + 0.5625 Reorder the terms: 0.5625 + 1.5v + v2 = 0.8333333333 + 0.5625 Combine like terms: 0.8333333333 + 0.5625 = 1.3958333333 0.5625 + 1.5v + v2 = 1.3958333333 Factor a perfect square on the left side: (v + 0.75)(v + 0.75) = 1.3958333333 Calculate the square root of the right side: 1.181453907 Break this problem into two subproblems by setting (v + 0.75) equal to 1.181453907 and -1.181453907.Subproblem 1
v + 0.75 = 1.181453907 Simplifying v + 0.75 = 1.181453907 Reorder the terms: 0.75 + v = 1.181453907 Solving 0.75 + v = 1.181453907 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 = 1.181453907 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + v = 1.181453907 + -0.75 v = 1.181453907 + -0.75 Combine like terms: 1.181453907 + -0.75 = 0.431453907 v = 0.431453907 Simplifying v = 0.431453907Subproblem 2
v + 0.75 = -1.181453907 Simplifying v + 0.75 = -1.181453907 Reorder the terms: 0.75 + v = -1.181453907 Solving 0.75 + v = -1.181453907 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 = -1.181453907 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + v = -1.181453907 + -0.75 v = -1.181453907 + -0.75 Combine like terms: -1.181453907 + -0.75 = -1.931453907 v = -1.931453907 Simplifying v = -1.931453907Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.431453907, -1.931453907}
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