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Simplifying 250 = 0.05v2 + 1.2v Reorder the terms: 250 = 1.2v + 0.05v2 Solving 250 = 1.2v + 0.05v2 Solving for variable 'v'. Reorder the terms: 250 + -1.2v + -0.05v2 = 1.2v + -1.2v + 0.05v2 + -0.05v2 Combine like terms: 1.2v + -1.2v = 0.0 250 + -1.2v + -0.05v2 = 0.0 + 0.05v2 + -0.05v2 250 + -1.2v + -0.05v2 = 0.05v2 + -0.05v2 Combine like terms: 0.05v2 + -0.05v2 = 0.00 250 + -1.2v + -0.05v2 = 0.00 Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -5000 + 24v + v2 = 0 Move the constant term to the right: Add '5000' to each side of the equation. -5000 + 24v + 5000 + v2 = 0 + 5000 Reorder the terms: -5000 + 5000 + 24v + v2 = 0 + 5000 Combine like terms: -5000 + 5000 = 0 0 + 24v + v2 = 0 + 5000 24v + v2 = 0 + 5000 Combine like terms: 0 + 5000 = 5000 24v + v2 = 5000 The v term is 24v. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24v + 144 + v2 = 5000 + 144 Reorder the terms: 144 + 24v + v2 = 5000 + 144 Combine like terms: 5000 + 144 = 5144 144 + 24v + v2 = 5144 Factor a perfect square on the left side: (v + 12)(v + 12) = 5144 Calculate the square root of the right side: 71.721684308 Break this problem into two subproblems by setting (v + 12) equal to 71.721684308 and -71.721684308.Subproblem 1
v + 12 = 71.721684308 Simplifying v + 12 = 71.721684308 Reorder the terms: 12 + v = 71.721684308 Solving 12 + v = 71.721684308 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + v = 71.721684308 + -12 Combine like terms: 12 + -12 = 0 0 + v = 71.721684308 + -12 v = 71.721684308 + -12 Combine like terms: 71.721684308 + -12 = 59.721684308 v = 59.721684308 Simplifying v = 59.721684308Subproblem 2
v + 12 = -71.721684308 Simplifying v + 12 = -71.721684308 Reorder the terms: 12 + v = -71.721684308 Solving 12 + v = -71.721684308 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + v = -71.721684308 + -12 Combine like terms: 12 + -12 = 0 0 + v = -71.721684308 + -12 v = -71.721684308 + -12 Combine like terms: -71.721684308 + -12 = -83.721684308 v = -83.721684308 Simplifying v = -83.721684308Solution
The solution to the problem is based on the solutions from the subproblems. v = {59.721684308, -83.721684308}
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