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Simplifying 0.05v2 + 1.1v + -65 = 0 Reorder the terms: -65 + 1.1v + 0.05v2 = 0 Solving -65 + 1.1v + 0.05v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. -1300 + 22v + v2 = 0 Move the constant term to the right: Add '1300' to each side of the equation. -1300 + 22v + 1300 + v2 = 0 + 1300 Reorder the terms: -1300 + 1300 + 22v + v2 = 0 + 1300 Combine like terms: -1300 + 1300 = 0 0 + 22v + v2 = 0 + 1300 22v + v2 = 0 + 1300 Combine like terms: 0 + 1300 = 1300 22v + v2 = 1300 The v term is 22v. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22v + 121 + v2 = 1300 + 121 Reorder the terms: 121 + 22v + v2 = 1300 + 121 Combine like terms: 1300 + 121 = 1421 121 + 22v + v2 = 1421 Factor a perfect square on the left side: (v + 11)(v + 11) = 1421 Calculate the square root of the right side: 37.69615365 Break this problem into two subproblems by setting (v + 11) equal to 37.69615365 and -37.69615365.Subproblem 1
v + 11 = 37.69615365 Simplifying v + 11 = 37.69615365 Reorder the terms: 11 + v = 37.69615365 Solving 11 + v = 37.69615365 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + v = 37.69615365 + -11 Combine like terms: 11 + -11 = 0 0 + v = 37.69615365 + -11 v = 37.69615365 + -11 Combine like terms: 37.69615365 + -11 = 26.69615365 v = 26.69615365 Simplifying v = 26.69615365Subproblem 2
v + 11 = -37.69615365 Simplifying v + 11 = -37.69615365 Reorder the terms: 11 + v = -37.69615365 Solving 11 + v = -37.69615365 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + v = -37.69615365 + -11 Combine like terms: 11 + -11 = 0 0 + v = -37.69615365 + -11 v = -37.69615365 + -11 Combine like terms: -37.69615365 + -11 = -48.69615365 v = -48.69615365 Simplifying v = -48.69615365Solution
The solution to the problem is based on the solutions from the subproblems. v = {26.69615365, -48.69615365}
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