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Simplifying 0.04v2 + 0.8v + -192 = 0 Reorder the terms: -192 + 0.8v + 0.04v2 = 0 Solving -192 + 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'. -4800 + 20v + v2 = 0 Move the constant term to the right: Add '4800' to each side of the equation. -4800 + 20v + 4800 + v2 = 0 + 4800 Reorder the terms: -4800 + 4800 + 20v + v2 = 0 + 4800 Combine like terms: -4800 + 4800 = 0 0 + 20v + v2 = 0 + 4800 20v + v2 = 0 + 4800 Combine like terms: 0 + 4800 = 4800 20v + v2 = 4800 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 = 4800 + 100 Reorder the terms: 100 + 20v + v2 = 4800 + 100 Combine like terms: 4800 + 100 = 4900 100 + 20v + v2 = 4900 Factor a perfect square on the left side: (v + 10)(v + 10) = 4900 Calculate the square root of the right side: 70 Break this problem into two subproblems by setting (v + 10) equal to 70 and -70.Subproblem 1
v + 10 = 70 Simplifying v + 10 = 70 Reorder the terms: 10 + v = 70 Solving 10 + v = 70 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 = 70 + -10 Combine like terms: 10 + -10 = 0 0 + v = 70 + -10 v = 70 + -10 Combine like terms: 70 + -10 = 60 v = 60 Simplifying v = 60Subproblem 2
v + 10 = -70 Simplifying v + 10 = -70 Reorder the terms: 10 + v = -70 Solving 10 + v = -70 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 = -70 + -10 Combine like terms: 10 + -10 = 0 0 + v = -70 + -10 v = -70 + -10 Combine like terms: -70 + -10 = -80 v = -80 Simplifying v = -80Solution
The solution to the problem is based on the solutions from the subproblems. v = {60, -80}
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