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Simplifying -2v2 + -5v = -5 Reorder the terms: -5v + -2v2 = -5 Solving -5v + -2v2 = -5 Solving for variable 'v'. Reorder the terms: 5 + -5v + -2v2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + -5v + -2v2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2.5 + 2.5v + v2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 2.5v + 2.5 + v2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 2.5v + v2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 2.5v + v2 = 0 + 2.5 2.5v + v2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 2.5v + v2 = 2.5 The v term is 2.5v. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5v + 1.5625 + v2 = 2.5 + 1.5625 Reorder the terms: 1.5625 + 2.5v + v2 = 2.5 + 1.5625 Combine like terms: 2.5 + 1.5625 = 4.0625 1.5625 + 2.5v + v2 = 4.0625 Factor a perfect square on the left side: (v + 1.25)(v + 1.25) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (v + 1.25) equal to 2.015564437 and -2.015564437.Subproblem 1
v + 1.25 = 2.015564437 Simplifying v + 1.25 = 2.015564437 Reorder the terms: 1.25 + v = 2.015564437 Solving 1.25 + v = 2.015564437 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + v = 2.015564437 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + v = 2.015564437 + -1.25 v = 2.015564437 + -1.25 Combine like terms: 2.015564437 + -1.25 = 0.765564437 v = 0.765564437 Simplifying v = 0.765564437Subproblem 2
v + 1.25 = -2.015564437 Simplifying v + 1.25 = -2.015564437 Reorder the terms: 1.25 + v = -2.015564437 Solving 1.25 + v = -2.015564437 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + v = -2.015564437 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + v = -2.015564437 + -1.25 v = -2.015564437 + -1.25 Combine like terms: -2.015564437 + -1.25 = -3.265564437 v = -3.265564437 Simplifying v = -3.265564437Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.765564437, -3.265564437}
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