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Simplifying 4v2 = 10v + -5 Reorder the terms: 4v2 = -5 + 10v Solving 4v2 = -5 + 10v Solving for variable 'v'. Reorder the terms: 5 + -10v + 4v2 = -5 + 10v + 5 + -10v Reorder the terms: 5 + -10v + 4v2 = -5 + 5 + 10v + -10v Combine like terms: -5 + 5 = 0 5 + -10v + 4v2 = 0 + 10v + -10v 5 + -10v + 4v2 = 10v + -10v Combine like terms: 10v + -10v = 0 5 + -10v + 4v2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + -2.5v + v2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -2.5v + -1.25 + v2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -2.5v + v2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -2.5v + v2 = 0 + -1.25 -2.5v + v2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -2.5v + v2 = -1.25 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 = -1.25 + 1.5625 Reorder the terms: 1.5625 + -2.5v + v2 = -1.25 + 1.5625 Combine like terms: -1.25 + 1.5625 = 0.3125 1.5625 + -2.5v + v2 = 0.3125 Factor a perfect square on the left side: (v + -1.25)(v + -1.25) = 0.3125 Calculate the square root of the right side: 0.559016994 Break this problem into two subproblems by setting (v + -1.25) equal to 0.559016994 and -0.559016994.Subproblem 1
v + -1.25 = 0.559016994 Simplifying v + -1.25 = 0.559016994 Reorder the terms: -1.25 + v = 0.559016994 Solving -1.25 + v = 0.559016994 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 = 0.559016994 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + v = 0.559016994 + 1.25 v = 0.559016994 + 1.25 Combine like terms: 0.559016994 + 1.25 = 1.809016994 v = 1.809016994 Simplifying v = 1.809016994Subproblem 2
v + -1.25 = -0.559016994 Simplifying v + -1.25 = -0.559016994 Reorder the terms: -1.25 + v = -0.559016994 Solving -1.25 + v = -0.559016994 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 = -0.559016994 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + v = -0.559016994 + 1.25 v = -0.559016994 + 1.25 Combine like terms: -0.559016994 + 1.25 = 0.690983006 v = 0.690983006 Simplifying v = 0.690983006Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.809016994, 0.690983006}
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