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Simplifying 5v2 + -26v = 2 Reorder the terms: -26v + 5v2 = 2 Solving -26v + 5v2 = 2 Solving for variable 'v'. Reorder the terms: -2 + -26v + 5v2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -26v + 5v2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -5.2v + v2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -5.2v + 0.4 + v2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -5.2v + v2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -5.2v + v2 = 0 + 0.4 -5.2v + v2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -5.2v + v2 = 0.4 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 = 0.4 + 6.76 Reorder the terms: 6.76 + -5.2v + v2 = 0.4 + 6.76 Combine like terms: 0.4 + 6.76 = 7.16 6.76 + -5.2v + v2 = 7.16 Factor a perfect square on the left side: (v + -2.6)(v + -2.6) = 7.16 Calculate the square root of the right side: 2.675817632 Break this problem into two subproblems by setting (v + -2.6) equal to 2.675817632 and -2.675817632.Subproblem 1
v + -2.6 = 2.675817632 Simplifying v + -2.6 = 2.675817632 Reorder the terms: -2.6 + v = 2.675817632 Solving -2.6 + v = 2.675817632 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 = 2.675817632 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + v = 2.675817632 + 2.6 v = 2.675817632 + 2.6 Combine like terms: 2.675817632 + 2.6 = 5.275817632 v = 5.275817632 Simplifying v = 5.275817632Subproblem 2
v + -2.6 = -2.675817632 Simplifying v + -2.6 = -2.675817632 Reorder the terms: -2.6 + v = -2.675817632 Solving -2.6 + v = -2.675817632 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 = -2.675817632 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + v = -2.675817632 + 2.6 v = -2.675817632 + 2.6 Combine like terms: -2.675817632 + 2.6 = -0.075817632 v = -0.075817632 Simplifying v = -0.075817632Solution
The solution to the problem is based on the solutions from the subproblems. v = {5.275817632, -0.075817632}
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