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Simplifying 9 = 0.03v + 0.003v2 Solving 9 = 0.03v + 0.003v2 Solving for variable 'v'. Reorder the terms: 9 + -0.03v + -0.003v2 = 0.03v + -0.03v + 0.003v2 + -0.003v2 Combine like terms: 0.03v + -0.03v = 0.00 9 + -0.03v + -0.003v2 = 0.00 + 0.003v2 + -0.003v2 9 + -0.03v + -0.003v2 = 0.003v2 + -0.003v2 Combine like terms: 0.003v2 + -0.003v2 = 0.000 9 + -0.03v + -0.003v2 = 0.000 Begin completing the square. Divide all terms by -0.003 the coefficient of the squared term: Divide each side by '-0.003'. -3000 + 10v + v2 = 0 Move the constant term to the right: Add '3000' to each side of the equation. -3000 + 10v + 3000 + v2 = 0 + 3000 Reorder the terms: -3000 + 3000 + 10v + v2 = 0 + 3000 Combine like terms: -3000 + 3000 = 0 0 + 10v + v2 = 0 + 3000 10v + v2 = 0 + 3000 Combine like terms: 0 + 3000 = 3000 10v + v2 = 3000 The v term is 10v. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10v + 25 + v2 = 3000 + 25 Reorder the terms: 25 + 10v + v2 = 3000 + 25 Combine like terms: 3000 + 25 = 3025 25 + 10v + v2 = 3025 Factor a perfect square on the left side: (v + 5)(v + 5) = 3025 Calculate the square root of the right side: 55 Break this problem into two subproblems by setting (v + 5) equal to 55 and -55.Subproblem 1
v + 5 = 55 Simplifying v + 5 = 55 Reorder the terms: 5 + v = 55 Solving 5 + v = 55 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + v = 55 + -5 Combine like terms: 5 + -5 = 0 0 + v = 55 + -5 v = 55 + -5 Combine like terms: 55 + -5 = 50 v = 50 Simplifying v = 50Subproblem 2
v + 5 = -55 Simplifying v + 5 = -55 Reorder the terms: 5 + v = -55 Solving 5 + v = -55 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + v = -55 + -5 Combine like terms: 5 + -5 = 0 0 + v = -55 + -5 v = -55 + -5 Combine like terms: -55 + -5 = -60 v = -60 Simplifying v = -60Solution
The solution to the problem is based on the solutions from the subproblems. v = {50, -60}
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