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Simplifying 0.4v2 + 2.5 = 2v Reorder the terms: 2.5 + 0.4v2 = 2v Solving 2.5 + 0.4v2 = 2v Solving for variable 'v'. Reorder the terms: 2.5 + -2v + 0.4v2 = 2v + -2v Combine like terms: 2v + -2v = 0 2.5 + -2v + 0.4v2 = 0 Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. 6.25 + -5v + v2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + -5v + -6.25 + v2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + -5v + v2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + -5v + v2 = 0 + -6.25 -5v + v2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 -5v + v2 = -6.25 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 = -6.25 + 6.25 Reorder the terms: 6.25 + -5v + v2 = -6.25 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 6.25 + -5v + v2 = 0.00 Factor a perfect square on the left side: (v + -2.5)(v + -2.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (v + -2.5) equal to 0.00 and 0.00.Subproblem 1
v + -2.5 = 0.00 Simplifying v + -2.5 = 0.00 Reorder the terms: -2.5 + v = 0.00 Solving -2.5 + v = 0.00 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 = 0.00 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + v = 0.00 + 2.5 v = 0.00 + 2.5 Combine like terms: 0.00 + 2.5 = 2.5 v = 2.5 Simplifying v = 2.5Subproblem 2
v + -2.5 = 0.00 Simplifying v + -2.5 = 0.00 Reorder the terms: -2.5 + v = 0.00 Solving -2.5 + v = 0.00 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 = 0.00 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + v = 0.00 + 2.5 v = 0.00 + 2.5 Combine like terms: 0.00 + 2.5 = 2.5 v = 2.5 Simplifying v = 2.5Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.5, 2.5}
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