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Simplifying 9v2 + -5 = -8v Reorder the terms: -5 + 9v2 = -8v Solving -5 + 9v2 = -8v Solving for variable 'v'. Reorder the terms: -5 + 8v + 9v2 = -8v + 8v Combine like terms: -8v + 8v = 0 -5 + 8v + 9v2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.5555555556 + 0.8888888889v + v2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + 0.8888888889v + 0.5555555556 + v2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + 0.8888888889v + v2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + 0.8888888889v + v2 = 0 + 0.5555555556 0.8888888889v + v2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 0.8888888889v + v2 = 0.5555555556 The v term is 0.8888888889v. Take half its coefficient (0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. 0.8888888889v + 0.1975308642 + v2 = 0.5555555556 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889v + v2 = 0.5555555556 + 0.1975308642 Combine like terms: 0.5555555556 + 0.1975308642 = 0.7530864198 0.1975308642 + 0.8888888889v + v2 = 0.7530864198 Factor a perfect square on the left side: (v + 0.4444444445)(v + 0.4444444445) = 0.7530864198 Calculate the square root of the right side: 0.86780552 Break this problem into two subproblems by setting (v + 0.4444444445) equal to 0.86780552 and -0.86780552.Subproblem 1
v + 0.4444444445 = 0.86780552 Simplifying v + 0.4444444445 = 0.86780552 Reorder the terms: 0.4444444445 + v = 0.86780552 Solving 0.4444444445 + v = 0.86780552 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + v = 0.86780552 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + v = 0.86780552 + -0.4444444445 v = 0.86780552 + -0.4444444445 Combine like terms: 0.86780552 + -0.4444444445 = 0.4233610755 v = 0.4233610755 Simplifying v = 0.4233610755Subproblem 2
v + 0.4444444445 = -0.86780552 Simplifying v + 0.4444444445 = -0.86780552 Reorder the terms: 0.4444444445 + v = -0.86780552 Solving 0.4444444445 + v = -0.86780552 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + v = -0.86780552 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + v = -0.86780552 + -0.4444444445 v = -0.86780552 + -0.4444444445 Combine like terms: -0.86780552 + -0.4444444445 = -1.3122499645 v = -1.3122499645 Simplifying v = -1.3122499645Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.4233610755, -1.3122499645}
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