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Simplifying 5v2 + -11v + -1 = 0 Reorder the terms: -1 + -11v + 5v2 = 0 Solving -1 + -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'. -0.2 + -2.2v + v2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -2.2v + 0.2 + v2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -2.2v + v2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -2.2v + v2 = 0 + 0.2 -2.2v + v2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -2.2v + v2 = 0.2 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 = 0.2 + 1.21 Reorder the terms: 1.21 + -2.2v + v2 = 0.2 + 1.21 Combine like terms: 0.2 + 1.21 = 1.41 1.21 + -2.2v + v2 = 1.41 Factor a perfect square on the left side: (v + -1.1)(v + -1.1) = 1.41 Calculate the square root of the right side: 1.187434209 Break this problem into two subproblems by setting (v + -1.1) equal to 1.187434209 and -1.187434209.Subproblem 1
v + -1.1 = 1.187434209 Simplifying v + -1.1 = 1.187434209 Reorder the terms: -1.1 + v = 1.187434209 Solving -1.1 + v = 1.187434209 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 = 1.187434209 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + v = 1.187434209 + 1.1 v = 1.187434209 + 1.1 Combine like terms: 1.187434209 + 1.1 = 2.287434209 v = 2.287434209 Simplifying v = 2.287434209Subproblem 2
v + -1.1 = -1.187434209 Simplifying v + -1.1 = -1.187434209 Reorder the terms: -1.1 + v = -1.187434209 Solving -1.1 + v = -1.187434209 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 = -1.187434209 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + v = -1.187434209 + 1.1 v = -1.187434209 + 1.1 Combine like terms: -1.187434209 + 1.1 = -0.087434209 v = -0.087434209 Simplifying v = -0.087434209Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.287434209, -0.087434209}
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