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Simplifying 100 = 0.04v2 + 11v Reorder the terms: 100 = 11v + 0.04v2 Solving 100 = 11v + 0.04v2 Solving for variable 'v'. Reorder the terms: 100 + -11v + -0.04v2 = 11v + -11v + 0.04v2 + -0.04v2 Combine like terms: 11v + -11v = 0 100 + -11v + -0.04v2 = 0 + 0.04v2 + -0.04v2 100 + -11v + -0.04v2 = 0.04v2 + -0.04v2 Combine like terms: 0.04v2 + -0.04v2 = 0.00 100 + -11v + -0.04v2 = 0.00 Begin completing the square. Divide all terms by -0.04 the coefficient of the squared term: Divide each side by '-0.04'. -2500 + 275v + v2 = 0 Move the constant term to the right: Add '2500' to each side of the equation. -2500 + 275v + 2500 + v2 = 0 + 2500 Reorder the terms: -2500 + 2500 + 275v + v2 = 0 + 2500 Combine like terms: -2500 + 2500 = 0 0 + 275v + v2 = 0 + 2500 275v + v2 = 0 + 2500 Combine like terms: 0 + 2500 = 2500 275v + v2 = 2500 The v term is 275v. Take half its coefficient (137.5). Square it (18906.25) and add it to both sides. Add '18906.25' to each side of the equation. 275v + 18906.25 + v2 = 2500 + 18906.25 Reorder the terms: 18906.25 + 275v + v2 = 2500 + 18906.25 Combine like terms: 2500 + 18906.25 = 21406.25 18906.25 + 275v + v2 = 21406.25 Factor a perfect square on the left side: (v + 137.5)(v + 137.5) = 21406.25 Calculate the square root of the right side: 146.308748884 Break this problem into two subproblems by setting (v + 137.5) equal to 146.308748884 and -146.308748884.Subproblem 1
v + 137.5 = 146.308748884 Simplifying v + 137.5 = 146.308748884 Reorder the terms: 137.5 + v = 146.308748884 Solving 137.5 + v = 146.308748884 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-137.5' to each side of the equation. 137.5 + -137.5 + v = 146.308748884 + -137.5 Combine like terms: 137.5 + -137.5 = 0.0 0.0 + v = 146.308748884 + -137.5 v = 146.308748884 + -137.5 Combine like terms: 146.308748884 + -137.5 = 8.808748884 v = 8.808748884 Simplifying v = 8.808748884Subproblem 2
v + 137.5 = -146.308748884 Simplifying v + 137.5 = -146.308748884 Reorder the terms: 137.5 + v = -146.308748884 Solving 137.5 + v = -146.308748884 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-137.5' to each side of the equation. 137.5 + -137.5 + v = -146.308748884 + -137.5 Combine like terms: 137.5 + -137.5 = 0.0 0.0 + v = -146.308748884 + -137.5 v = -146.308748884 + -137.5 Combine like terms: -146.308748884 + -137.5 = -283.808748884 v = -283.808748884 Simplifying v = -283.808748884Solution
The solution to the problem is based on the solutions from the subproblems. v = {8.808748884, -283.808748884}
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