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Simplifying 9v2 + -1v + -20 = 0 Reorder the terms: -20 + -1v + 9v2 = 0 Solving -20 + -1v + 9v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.222222222 + -0.1111111111v + v2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + -0.1111111111v + 2.222222222 + v2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + -0.1111111111v + v2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + -0.1111111111v + v2 = 0 + 2.222222222 -0.1111111111v + v2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 -0.1111111111v + v2 = 2.222222222 The v term is -0.1111111111v. Take half its coefficient (-0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. -0.1111111111v + 0.003086419752 + v2 = 2.222222222 + 0.003086419752 Reorder the terms: 0.003086419752 + -0.1111111111v + v2 = 2.222222222 + 0.003086419752 Combine like terms: 2.222222222 + 0.003086419752 = 2.225308641752 0.003086419752 + -0.1111111111v + v2 = 2.225308641752 Factor a perfect square on the left side: (v + -0.05555555555)(v + -0.05555555555) = 2.225308641752 Calculate the square root of the right side: 1.491746842 Break this problem into two subproblems by setting (v + -0.05555555555) equal to 1.491746842 and -1.491746842.Subproblem 1
v + -0.05555555555 = 1.491746842 Simplifying v + -0.05555555555 = 1.491746842 Reorder the terms: -0.05555555555 + v = 1.491746842 Solving -0.05555555555 + v = 1.491746842 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + v = 1.491746842 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + v = 1.491746842 + 0.05555555555 v = 1.491746842 + 0.05555555555 Combine like terms: 1.491746842 + 0.05555555555 = 1.54730239755 v = 1.54730239755 Simplifying v = 1.54730239755Subproblem 2
v + -0.05555555555 = -1.491746842 Simplifying v + -0.05555555555 = -1.491746842 Reorder the terms: -0.05555555555 + v = -1.491746842 Solving -0.05555555555 + v = -1.491746842 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + v = -1.491746842 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + v = -1.491746842 + 0.05555555555 v = -1.491746842 + 0.05555555555 Combine like terms: -1.491746842 + 0.05555555555 = -1.43619128645 v = -1.43619128645 Simplifying v = -1.43619128645Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.54730239755, -1.43619128645}
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