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Simplifying 5v2 + 26v + -41 = 0 Reorder the terms: -41 + 26v + 5v2 = 0 Solving -41 + 26v + 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'. -8.2 + 5.2v + v2 = 0 Move the constant term to the right: Add '8.2' to each side of the equation. -8.2 + 5.2v + 8.2 + v2 = 0 + 8.2 Reorder the terms: -8.2 + 8.2 + 5.2v + v2 = 0 + 8.2 Combine like terms: -8.2 + 8.2 = 0.0 0.0 + 5.2v + v2 = 0 + 8.2 5.2v + v2 = 0 + 8.2 Combine like terms: 0 + 8.2 = 8.2 5.2v + v2 = 8.2 The v term is 5.2v. Take half its coefficient (2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. 5.2v + 6.76 + v2 = 8.2 + 6.76 Reorder the terms: 6.76 + 5.2v + v2 = 8.2 + 6.76 Combine like terms: 8.2 + 6.76 = 14.96 6.76 + 5.2v + v2 = 14.96 Factor a perfect square on the left side: (v + 2.6)(v + 2.6) = 14.96 Calculate the square root of the right side: 3.867815921 Break this problem into two subproblems by setting (v + 2.6) equal to 3.867815921 and -3.867815921.Subproblem 1
v + 2.6 = 3.867815921 Simplifying v + 2.6 = 3.867815921 Reorder the terms: 2.6 + v = 3.867815921 Solving 2.6 + v = 3.867815921 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + v = 3.867815921 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + v = 3.867815921 + -2.6 v = 3.867815921 + -2.6 Combine like terms: 3.867815921 + -2.6 = 1.267815921 v = 1.267815921 Simplifying v = 1.267815921Subproblem 2
v + 2.6 = -3.867815921 Simplifying v + 2.6 = -3.867815921 Reorder the terms: 2.6 + v = -3.867815921 Solving 2.6 + v = -3.867815921 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + v = -3.867815921 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + v = -3.867815921 + -2.6 v = -3.867815921 + -2.6 Combine like terms: -3.867815921 + -2.6 = -6.467815921 v = -6.467815921 Simplifying v = -6.467815921Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.267815921, -6.467815921}
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