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Simplifying 187.5 = 0.75v + 0.06v2 Solving 187.5 = 0.75v + 0.06v2 Solving for variable 'v'. Reorder the terms: 187.5 + -0.75v + -0.06v2 = 0.75v + -0.75v + 0.06v2 + -0.06v2 Combine like terms: 0.75v + -0.75v = 0.00 187.5 + -0.75v + -0.06v2 = 0.00 + 0.06v2 + -0.06v2 187.5 + -0.75v + -0.06v2 = 0.06v2 + -0.06v2 Combine like terms: 0.06v2 + -0.06v2 = 0.00 187.5 + -0.75v + -0.06v2 = 0.00 Begin completing the square. Divide all terms by -0.06 the coefficient of the squared term: Divide each side by '-0.06'. -3125 + 12.5v + v2 = 0 Move the constant term to the right: Add '3125' to each side of the equation. -3125 + 12.5v + 3125 + v2 = 0 + 3125 Reorder the terms: -3125 + 3125 + 12.5v + v2 = 0 + 3125 Combine like terms: -3125 + 3125 = 0 0 + 12.5v + v2 = 0 + 3125 12.5v + v2 = 0 + 3125 Combine like terms: 0 + 3125 = 3125 12.5v + v2 = 3125 The v term is 12.5v. Take half its coefficient (6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. 12.5v + 39.0625 + v2 = 3125 + 39.0625 Reorder the terms: 39.0625 + 12.5v + v2 = 3125 + 39.0625 Combine like terms: 3125 + 39.0625 = 3164.0625 39.0625 + 12.5v + v2 = 3164.0625 Factor a perfect square on the left side: (v + 6.25)(v + 6.25) = 3164.0625 Calculate the square root of the right side: 56.25 Break this problem into two subproblems by setting (v + 6.25) equal to 56.25 and -56.25.Subproblem 1
v + 6.25 = 56.25 Simplifying v + 6.25 = 56.25 Reorder the terms: 6.25 + v = 56.25 Solving 6.25 + v = 56.25 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + v = 56.25 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + v = 56.25 + -6.25 v = 56.25 + -6.25 Combine like terms: 56.25 + -6.25 = 50 v = 50 Simplifying v = 50Subproblem 2
v + 6.25 = -56.25 Simplifying v + 6.25 = -56.25 Reorder the terms: 6.25 + v = -56.25 Solving 6.25 + v = -56.25 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + v = -56.25 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + v = -56.25 + -6.25 v = -56.25 + -6.25 Combine like terms: -56.25 + -6.25 = -62.5 v = -62.5 Simplifying v = -62.5Solution
The solution to the problem is based on the solutions from the subproblems. v = {50, -62.5}
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