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Simplifying 5v2 + 11v + -2 = 0 Reorder the terms: -2 + 11v + 5v2 = 0 Solving -2 + 11v + 5v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + 2.2v + v2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 2.2v + 0.4 + v2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 2.2v + v2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 2.2v + v2 = 0 + 0.4 2.2v + v2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 2.2v + v2 = 0.4 The v term is 2.2v. Take half its coefficient (1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. 2.2v + 1.21 + v2 = 0.4 + 1.21 Reorder the terms: 1.21 + 2.2v + v2 = 0.4 + 1.21 Combine like terms: 0.4 + 1.21 = 1.61 1.21 + 2.2v + v2 = 1.61 Factor a perfect square on the left side: (v + 1.1)(v + 1.1) = 1.61 Calculate the square root of the right side: 1.268857754 Break this problem into two subproblems by setting (v + 1.1) equal to 1.268857754 and -1.268857754.Subproblem 1
v + 1.1 = 1.268857754 Simplifying v + 1.1 = 1.268857754 Reorder the terms: 1.1 + v = 1.268857754 Solving 1.1 + v = 1.268857754 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + v = 1.268857754 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + v = 1.268857754 + -1.1 v = 1.268857754 + -1.1 Combine like terms: 1.268857754 + -1.1 = 0.168857754 v = 0.168857754 Simplifying v = 0.168857754Subproblem 2
v + 1.1 = -1.268857754 Simplifying v + 1.1 = -1.268857754 Reorder the terms: 1.1 + v = -1.268857754 Solving 1.1 + v = -1.268857754 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + v = -1.268857754 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + v = -1.268857754 + -1.1 v = -1.268857754 + -1.1 Combine like terms: -1.268857754 + -1.1 = -2.368857754 v = -2.368857754 Simplifying v = -2.368857754Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.168857754, -2.368857754}
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