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Simplifying 2v2 + 2v = 23 Reorder the terms: 2v + 2v2 = 23 Solving 2v + 2v2 = 23 Solving for variable 'v'. Reorder the terms: -23 + 2v + 2v2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + 2v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -11.5 + v + v2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + v + 11.5 + v2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + v + v2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + v + v2 = 0 + 11.5 v + v2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 v + v2 = 11.5 The v term is v. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + v2 = 11.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + v2 = 11.5 + 0.25 Combine like terms: 11.5 + 0.25 = 11.75 1.25 + v2 = 11.75 Factor a perfect square on the left side: (v + 0.5)(v + 0.5) = 11.75 Calculate the square root of the right side: 3.4278273 Break this problem into two subproblems by setting (v + 0.5) equal to 3.4278273 and -3.4278273.Subproblem 1
v + 0.5 = 3.4278273 Simplifying v + 0.5 = 3.4278273 Reorder the terms: 0.5 + v = 3.4278273 Solving 0.5 + v = 3.4278273 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + v = 3.4278273 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = 3.4278273 + -0.5 v = 3.4278273 + -0.5 Combine like terms: 3.4278273 + -0.5 = 2.9278273 v = 2.9278273 Simplifying v = 2.9278273Subproblem 2
v + 0.5 = -3.4278273 Simplifying v + 0.5 = -3.4278273 Reorder the terms: 0.5 + v = -3.4278273 Solving 0.5 + v = -3.4278273 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + v = -3.4278273 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = -3.4278273 + -0.5 v = -3.4278273 + -0.5 Combine like terms: -3.4278273 + -0.5 = -3.9278273 v = -3.9278273 Simplifying v = -3.9278273Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.9278273, -3.9278273}
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