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Simplifying 5v2 + -39v + 40 = 0 Reorder the terms: 40 + -39v + 5v2 = 0 Solving 40 + -39v + 5v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 8 + -7.8v + v2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -7.8v + -8 + v2 = 0 + -8 Reorder the terms: 8 + -8 + -7.8v + v2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7.8v + v2 = 0 + -8 -7.8v + v2 = 0 + -8 Combine like terms: 0 + -8 = -8 -7.8v + v2 = -8 The v term is -7.8v. Take half its coefficient (-3.9). Square it (15.21) and add it to both sides. Add '15.21' to each side of the equation. -7.8v + 15.21 + v2 = -8 + 15.21 Reorder the terms: 15.21 + -7.8v + v2 = -8 + 15.21 Combine like terms: -8 + 15.21 = 7.21 15.21 + -7.8v + v2 = 7.21 Factor a perfect square on the left side: (v + -3.9)(v + -3.9) = 7.21 Calculate the square root of the right side: 2.685144316 Break this problem into two subproblems by setting (v + -3.9) equal to 2.685144316 and -2.685144316.Subproblem 1
v + -3.9 = 2.685144316 Simplifying v + -3.9 = 2.685144316 Reorder the terms: -3.9 + v = 2.685144316 Solving -3.9 + v = 2.685144316 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.9' to each side of the equation. -3.9 + 3.9 + v = 2.685144316 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + v = 2.685144316 + 3.9 v = 2.685144316 + 3.9 Combine like terms: 2.685144316 + 3.9 = 6.585144316 v = 6.585144316 Simplifying v = 6.585144316Subproblem 2
v + -3.9 = -2.685144316 Simplifying v + -3.9 = -2.685144316 Reorder the terms: -3.9 + v = -2.685144316 Solving -3.9 + v = -2.685144316 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.9' to each side of the equation. -3.9 + 3.9 + v = -2.685144316 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + v = -2.685144316 + 3.9 v = -2.685144316 + 3.9 Combine like terms: -2.685144316 + 3.9 = 1.214855684 v = 1.214855684 Simplifying v = 1.214855684Solution
The solution to the problem is based on the solutions from the subproblems. v = {6.585144316, 1.214855684}
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