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Simplifying v2 + -5v + -3.6 = 0 Reorder the terms: -3.6 + -5v + v2 = 0 Solving -3.6 + -5v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + -5v + 3.6 + v2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + -5v + v2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + -5v + v2 = 0 + 3.6 -5v + v2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 -5v + v2 = 3.6 The v term is -5v. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5v + 6.25 + v2 = 3.6 + 6.25 Reorder the terms: 6.25 + -5v + v2 = 3.6 + 6.25 Combine like terms: 3.6 + 6.25 = 9.85 6.25 + -5v + v2 = 9.85 Factor a perfect square on the left side: (v + -2.5)(v + -2.5) = 9.85 Calculate the square root of the right side: 3.138470965 Break this problem into two subproblems by setting (v + -2.5) equal to 3.138470965 and -3.138470965.Subproblem 1
v + -2.5 = 3.138470965 Simplifying v + -2.5 = 3.138470965 Reorder the terms: -2.5 + v = 3.138470965 Solving -2.5 + v = 3.138470965 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + v = 3.138470965 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + v = 3.138470965 + 2.5 v = 3.138470965 + 2.5 Combine like terms: 3.138470965 + 2.5 = 5.638470965 v = 5.638470965 Simplifying v = 5.638470965Subproblem 2
v + -2.5 = -3.138470965 Simplifying v + -2.5 = -3.138470965 Reorder the terms: -2.5 + v = -3.138470965 Solving -2.5 + v = -3.138470965 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + v = -3.138470965 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + v = -3.138470965 + 2.5 v = -3.138470965 + 2.5 Combine like terms: -3.138470965 + 2.5 = -0.638470965 v = -0.638470965 Simplifying v = -0.638470965Solution
The solution to the problem is based on the solutions from the subproblems. v = {5.638470965, -0.638470965}
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