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Simplifying -2v + 2 = 9v2 Reorder the terms: 2 + -2v = 9v2 Solving 2 + -2v = 9v2 Solving for variable 'v'. Combine like terms: 9v2 + -9v2 = 0 2 + -2v + -9v2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.2222222222 + 0.2222222222v + v2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222v + 0.2222222222 + v2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + 0.2222222222v + v2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + 0.2222222222v + v2 = 0 + 0.2222222222 0.2222222222v + v2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 0.2222222222v + v2 = 0.2222222222 The v term is 0.2222222222v. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222v + 0.01234567901 + v2 = 0.2222222222 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222v + v2 = 0.2222222222 + 0.01234567901 Combine like terms: 0.2222222222 + 0.01234567901 = 0.23456790121 0.01234567901 + 0.2222222222v + v2 = 0.23456790121 Factor a perfect square on the left side: (v + 0.1111111111)(v + 0.1111111111) = 0.23456790121 Calculate the square root of the right side: 0.484322105 Break this problem into two subproblems by setting (v + 0.1111111111) equal to 0.484322105 and -0.484322105.Subproblem 1
v + 0.1111111111 = 0.484322105 Simplifying v + 0.1111111111 = 0.484322105 Reorder the terms: 0.1111111111 + v = 0.484322105 Solving 0.1111111111 + v = 0.484322105 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + v = 0.484322105 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + v = 0.484322105 + -0.1111111111 v = 0.484322105 + -0.1111111111 Combine like terms: 0.484322105 + -0.1111111111 = 0.3732109939 v = 0.3732109939 Simplifying v = 0.3732109939Subproblem 2
v + 0.1111111111 = -0.484322105 Simplifying v + 0.1111111111 = -0.484322105 Reorder the terms: 0.1111111111 + v = -0.484322105 Solving 0.1111111111 + v = -0.484322105 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + v = -0.484322105 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + v = -0.484322105 + -0.1111111111 v = -0.484322105 + -0.1111111111 Combine like terms: -0.484322105 + -0.1111111111 = -0.5954332161 v = -0.5954332161 Simplifying v = -0.5954332161Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.3732109939, -0.5954332161}
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