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Simplifying 0.02v2 + 2.2v + -439 = 0 Reorder the terms: -439 + 2.2v + 0.02v2 = 0 Solving -439 + 2.2v + 0.02v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. -21950 + 110v + v2 = 0 Move the constant term to the right: Add '21950' to each side of the equation. -21950 + 110v + 21950 + v2 = 0 + 21950 Reorder the terms: -21950 + 21950 + 110v + v2 = 0 + 21950 Combine like terms: -21950 + 21950 = 0 0 + 110v + v2 = 0 + 21950 110v + v2 = 0 + 21950 Combine like terms: 0 + 21950 = 21950 110v + v2 = 21950 The v term is 110v. Take half its coefficient (55). Square it (3025) and add it to both sides. Add '3025' to each side of the equation. 110v + 3025 + v2 = 21950 + 3025 Reorder the terms: 3025 + 110v + v2 = 21950 + 3025 Combine like terms: 21950 + 3025 = 24975 3025 + 110v + v2 = 24975 Factor a perfect square on the left side: (v + 55)(v + 55) = 24975 Calculate the square root of the right side: 158.034806293 Break this problem into two subproblems by setting (v + 55) equal to 158.034806293 and -158.034806293.Subproblem 1
v + 55 = 158.034806293 Simplifying v + 55 = 158.034806293 Reorder the terms: 55 + v = 158.034806293 Solving 55 + v = 158.034806293 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-55' to each side of the equation. 55 + -55 + v = 158.034806293 + -55 Combine like terms: 55 + -55 = 0 0 + v = 158.034806293 + -55 v = 158.034806293 + -55 Combine like terms: 158.034806293 + -55 = 103.034806293 v = 103.034806293 Simplifying v = 103.034806293Subproblem 2
v + 55 = -158.034806293 Simplifying v + 55 = -158.034806293 Reorder the terms: 55 + v = -158.034806293 Solving 55 + v = -158.034806293 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-55' to each side of the equation. 55 + -55 + v = -158.034806293 + -55 Combine like terms: 55 + -55 = 0 0 + v = -158.034806293 + -55 v = -158.034806293 + -55 Combine like terms: -158.034806293 + -55 = -213.034806293 v = -213.034806293 Simplifying v = -213.034806293Solution
The solution to the problem is based on the solutions from the subproblems. v = {103.034806293, -213.034806293}
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