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Simplifying 4v2 + -20v + -5 = 0 Reorder the terms: -5 + -20v + 4v2 = 0 Solving -5 + -20v + 4v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -5v + v2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -5v + 1.25 + v2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -5v + v2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -5v + v2 = 0 + 1.25 -5v + v2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -5v + v2 = 1.25 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 = 1.25 + 6.25 Reorder the terms: 6.25 + -5v + v2 = 1.25 + 6.25 Combine like terms: 1.25 + 6.25 = 7.5 6.25 + -5v + v2 = 7.5 Factor a perfect square on the left side: (v + -2.5)(v + -2.5) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (v + -2.5) equal to 2.738612788 and -2.738612788.Subproblem 1
v + -2.5 = 2.738612788 Simplifying v + -2.5 = 2.738612788 Reorder the terms: -2.5 + v = 2.738612788 Solving -2.5 + v = 2.738612788 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 = 2.738612788 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + v = 2.738612788 + 2.5 v = 2.738612788 + 2.5 Combine like terms: 2.738612788 + 2.5 = 5.238612788 v = 5.238612788 Simplifying v = 5.238612788Subproblem 2
v + -2.5 = -2.738612788 Simplifying v + -2.5 = -2.738612788 Reorder the terms: -2.5 + v = -2.738612788 Solving -2.5 + v = -2.738612788 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 = -2.738612788 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + v = -2.738612788 + 2.5 v = -2.738612788 + 2.5 Combine like terms: -2.738612788 + 2.5 = -0.238612788 v = -0.238612788 Simplifying v = -0.238612788Solution
The solution to the problem is based on the solutions from the subproblems. v = {5.238612788, -0.238612788}
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