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Simplifying 100v2 + -220v = 121 Reorder the terms: -220v + 100v2 = 121 Solving -220v + 100v2 = 121 Solving for variable 'v'. Reorder the terms: -121 + -220v + 100v2 = 121 + -121 Combine like terms: 121 + -121 = 0 -121 + -220v + 100v2 = 0 Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. -1.21 + -2.2v + v2 = 0 Move the constant term to the right: Add '1.21' to each side of the equation. -1.21 + -2.2v + 1.21 + v2 = 0 + 1.21 Reorder the terms: -1.21 + 1.21 + -2.2v + v2 = 0 + 1.21 Combine like terms: -1.21 + 1.21 = 0.00 0.00 + -2.2v + v2 = 0 + 1.21 -2.2v + v2 = 0 + 1.21 Combine like terms: 0 + 1.21 = 1.21 -2.2v + v2 = 1.21 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 = 1.21 + 1.21 Reorder the terms: 1.21 + -2.2v + v2 = 1.21 + 1.21 Combine like terms: 1.21 + 1.21 = 2.42 1.21 + -2.2v + v2 = 2.42 Factor a perfect square on the left side: (v + -1.1)(v + -1.1) = 2.42 Calculate the square root of the right side: 1.555634919 Break this problem into two subproblems by setting (v + -1.1) equal to 1.555634919 and -1.555634919.Subproblem 1
v + -1.1 = 1.555634919 Simplifying v + -1.1 = 1.555634919 Reorder the terms: -1.1 + v = 1.555634919 Solving -1.1 + v = 1.555634919 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 = 1.555634919 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + v = 1.555634919 + 1.1 v = 1.555634919 + 1.1 Combine like terms: 1.555634919 + 1.1 = 2.655634919 v = 2.655634919 Simplifying v = 2.655634919Subproblem 2
v + -1.1 = -1.555634919 Simplifying v + -1.1 = -1.555634919 Reorder the terms: -1.1 + v = -1.555634919 Solving -1.1 + v = -1.555634919 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 = -1.555634919 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + v = -1.555634919 + 1.1 v = -1.555634919 + 1.1 Combine like terms: -1.555634919 + 1.1 = -0.455634919 v = -0.455634919 Simplifying v = -0.455634919Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.655634919, -0.455634919}
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