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Simplifying 5v2 + v + 0.4 = 0 Reorder the terms: 0.4 + v + 5v2 = 0 Solving 0.4 + v + 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'. 0.08 + 0.2v + v2 = 0 Move the constant term to the right: Add '-0.08' to each side of the equation. 0.08 + 0.2v + -0.08 + v2 = 0 + -0.08 Reorder the terms: 0.08 + -0.08 + 0.2v + v2 = 0 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + 0.2v + v2 = 0 + -0.08 0.2v + v2 = 0 + -0.08 Combine like terms: 0 + -0.08 = -0.08 0.2v + v2 = -0.08 The v term is v. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.2v + 0.25 + v2 = -0.08 + 0.25 Reorder the terms: 0.25 + 0.2v + v2 = -0.08 + 0.25 Combine like terms: -0.08 + 0.25 = 0.17 0.25 + 0.2v + v2 = 0.17 Factor a perfect square on the left side: (v + 0.5)(v + 0.5) = 0.17 Calculate the square root of the right side: 0.412310563 Break this problem into two subproblems by setting (v + 0.5) equal to 0.412310563 and -0.412310563.Subproblem 1
v + 0.5 = 0.412310563 Simplifying v + 0.5 = 0.412310563 Reorder the terms: 0.5 + v = 0.412310563 Solving 0.5 + v = 0.412310563 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + v = 0.412310563 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = 0.412310563 + -0.5 v = 0.412310563 + -0.5 Combine like terms: 0.412310563 + -0.5 = -0.087689437 v = -0.087689437 Simplifying v = -0.087689437Subproblem 2
v + 0.5 = -0.412310563 Simplifying v + 0.5 = -0.412310563 Reorder the terms: 0.5 + v = -0.412310563 Solving 0.5 + v = -0.412310563 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + v = -0.412310563 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = -0.412310563 + -0.5 v = -0.412310563 + -0.5 Combine like terms: -0.412310563 + -0.5 = -0.912310563 v = -0.912310563 Simplifying v = -0.912310563Solution
The solution to the problem is based on the solutions from the subproblems. v = {-0.087689437, -0.912310563}
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