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Simplifying 0.05v2 + 0.4v + -15 = 0 Reorder the terms: -15 + 0.4v + 0.05v2 = 0 Solving -15 + 0.4v + 0.05v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. -300 + 8v + v2 = 0 Move the constant term to the right: Add '300' to each side of the equation. -300 + 8v + 300 + v2 = 0 + 300 Reorder the terms: -300 + 300 + 8v + v2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 8v + v2 = 0 + 300 8v + v2 = 0 + 300 Combine like terms: 0 + 300 = 300 8v + v2 = 300 The v term is 8v. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8v + 16 + v2 = 300 + 16 Reorder the terms: 16 + 8v + v2 = 300 + 16 Combine like terms: 300 + 16 = 316 16 + 8v + v2 = 316 Factor a perfect square on the left side: (v + 4)(v + 4) = 316 Calculate the square root of the right side: 17.776388835 Break this problem into two subproblems by setting (v + 4) equal to 17.776388835 and -17.776388835.Subproblem 1
v + 4 = 17.776388835 Simplifying v + 4 = 17.776388835 Reorder the terms: 4 + v = 17.776388835 Solving 4 + v = 17.776388835 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + v = 17.776388835 + -4 Combine like terms: 4 + -4 = 0 0 + v = 17.776388835 + -4 v = 17.776388835 + -4 Combine like terms: 17.776388835 + -4 = 13.776388835 v = 13.776388835 Simplifying v = 13.776388835Subproblem 2
v + 4 = -17.776388835 Simplifying v + 4 = -17.776388835 Reorder the terms: 4 + v = -17.776388835 Solving 4 + v = -17.776388835 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + v = -17.776388835 + -4 Combine like terms: 4 + -4 = 0 0 + v = -17.776388835 + -4 v = -17.776388835 + -4 Combine like terms: -17.776388835 + -4 = -21.776388835 v = -21.776388835 Simplifying v = -21.776388835Solution
The solution to the problem is based on the solutions from the subproblems. v = {13.776388835, -21.776388835}
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