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Simplifying 4v2 + 20v + 11 = 0 Reorder the terms: 11 + 20v + 4v2 = 0 Solving 11 + 20v + 4v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.75 + 5v + v2 = 0 Move the constant term to the right: Add '-2.75' to each side of the equation. 2.75 + 5v + -2.75 + v2 = 0 + -2.75 Reorder the terms: 2.75 + -2.75 + 5v + v2 = 0 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + 5v + v2 = 0 + -2.75 5v + v2 = 0 + -2.75 Combine like terms: 0 + -2.75 = -2.75 5v + v2 = -2.75 The v term is 5v. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5v + 6.25 + v2 = -2.75 + 6.25 Reorder the terms: 6.25 + 5v + v2 = -2.75 + 6.25 Combine like terms: -2.75 + 6.25 = 3.5 6.25 + 5v + v2 = 3.5 Factor a perfect square on the left side: (v + 2.5)(v + 2.5) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (v + 2.5) equal to 1.870828693 and -1.870828693.Subproblem 1
v + 2.5 = 1.870828693 Simplifying v + 2.5 = 1.870828693 Reorder the terms: 2.5 + v = 1.870828693 Solving 2.5 + v = 1.870828693 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + v = 1.870828693 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + v = 1.870828693 + -2.5 v = 1.870828693 + -2.5 Combine like terms: 1.870828693 + -2.5 = -0.629171307 v = -0.629171307 Simplifying v = -0.629171307Subproblem 2
v + 2.5 = -1.870828693 Simplifying v + 2.5 = -1.870828693 Reorder the terms: 2.5 + v = -1.870828693 Solving 2.5 + v = -1.870828693 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + v = -1.870828693 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + v = -1.870828693 + -2.5 v = -1.870828693 + -2.5 Combine like terms: -1.870828693 + -2.5 = -4.370828693 v = -4.370828693 Simplifying v = -4.370828693Solution
The solution to the problem is based on the solutions from the subproblems. v = {-0.629171307, -4.370828693}
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