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Simplifying 0.04v2 + 0.8v + -96 = 0 Reorder the terms: -96 + 0.8v + 0.04v2 = 0 Solving -96 + 0.8v + 0.04v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. -2400 + 20v + v2 = 0 Move the constant term to the right: Add '2400' to each side of the equation. -2400 + 20v + 2400 + v2 = 0 + 2400 Reorder the terms: -2400 + 2400 + 20v + v2 = 0 + 2400 Combine like terms: -2400 + 2400 = 0 0 + 20v + v2 = 0 + 2400 20v + v2 = 0 + 2400 Combine like terms: 0 + 2400 = 2400 20v + v2 = 2400 The v term is 20v. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20v + 100 + v2 = 2400 + 100 Reorder the terms: 100 + 20v + v2 = 2400 + 100 Combine like terms: 2400 + 100 = 2500 100 + 20v + v2 = 2500 Factor a perfect square on the left side: (v + 10)(v + 10) = 2500 Calculate the square root of the right side: 50 Break this problem into two subproblems by setting (v + 10) equal to 50 and -50.Subproblem 1
v + 10 = 50 Simplifying v + 10 = 50 Reorder the terms: 10 + v = 50 Solving 10 + v = 50 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + v = 50 + -10 Combine like terms: 10 + -10 = 0 0 + v = 50 + -10 v = 50 + -10 Combine like terms: 50 + -10 = 40 v = 40 Simplifying v = 40Subproblem 2
v + 10 = -50 Simplifying v + 10 = -50 Reorder the terms: 10 + v = -50 Solving 10 + v = -50 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + v = -50 + -10 Combine like terms: 10 + -10 = 0 0 + v = -50 + -10 v = -50 + -10 Combine like terms: -50 + -10 = -60 v = -60 Simplifying v = -60Solution
The solution to the problem is based on the solutions from the subproblems. v = {40, -60}
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