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Simplifying 0.0066 = 0.000113v + 0.0000044v2 Solving 0.0066 = 0.000113v + 0.0000044v2 Solving for variable 'v'. Reorder the terms: 0.0066 + -0.000113v + -0.0000044v2 = 0.000113v + -0.000113v + 0.0000044v2 + -0.0000044v2 Combine like terms: 0.000113v + -0.000113v = 0.000000 0.0066 + -0.000113v + -0.0000044v2 = 0.000000 + 0.0000044v2 + -0.0000044v2 0.0066 + -0.000113v + -0.0000044v2 = 0.0000044v2 + -0.0000044v2 Combine like terms: 0.0000044v2 + -0.0000044v2 = 0.0000000 0.0066 + -0.000113v + -0.0000044v2 = 0.0000000 Begin completing the square. Divide all terms by -0.0000044 the coefficient of the squared term: Divide each side by '-0.0000044'. -1500 + 25.68181818v + v2 = 0 Move the constant term to the right: Add '1500' to each side of the equation. -1500 + 25.68181818v + 1500 + v2 = 0 + 1500 Reorder the terms: -1500 + 1500 + 25.68181818v + v2 = 0 + 1500 Combine like terms: -1500 + 1500 = 0 0 + 25.68181818v + v2 = 0 + 1500 25.68181818v + v2 = 0 + 1500 Combine like terms: 0 + 1500 = 1500 25.68181818v + v2 = 1500 The v term is 25.68181818v. Take half its coefficient (12.84090909). Square it (164.8889463) and add it to both sides. Add '164.8889463' to each side of the equation. 25.68181818v + 164.8889463 + v2 = 1500 + 164.8889463 Reorder the terms: 164.8889463 + 25.68181818v + v2 = 1500 + 164.8889463 Combine like terms: 1500 + 164.8889463 = 1664.8889463 164.8889463 + 25.68181818v + v2 = 1664.8889463 Factor a perfect square on the left side: (v + 12.84090909)(v + 12.84090909) = 1664.8889463 Calculate the square root of the right side: 40.803050698 Break this problem into two subproblems by setting (v + 12.84090909) equal to 40.803050698 and -40.803050698.Subproblem 1
v + 12.84090909 = 40.803050698 Simplifying v + 12.84090909 = 40.803050698 Reorder the terms: 12.84090909 + v = 40.803050698 Solving 12.84090909 + v = 40.803050698 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-12.84090909' to each side of the equation. 12.84090909 + -12.84090909 + v = 40.803050698 + -12.84090909 Combine like terms: 12.84090909 + -12.84090909 = 0.00000000 0.00000000 + v = 40.803050698 + -12.84090909 v = 40.803050698 + -12.84090909 Combine like terms: 40.803050698 + -12.84090909 = 27.962141608 v = 27.962141608 Simplifying v = 27.962141608Subproblem 2
v + 12.84090909 = -40.803050698 Simplifying v + 12.84090909 = -40.803050698 Reorder the terms: 12.84090909 + v = -40.803050698 Solving 12.84090909 + v = -40.803050698 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-12.84090909' to each side of the equation. 12.84090909 + -12.84090909 + v = -40.803050698 + -12.84090909 Combine like terms: 12.84090909 + -12.84090909 = 0.00000000 0.00000000 + v = -40.803050698 + -12.84090909 v = -40.803050698 + -12.84090909 Combine like terms: -40.803050698 + -12.84090909 = -53.643959788 v = -53.643959788 Simplifying v = -53.643959788Solution
The solution to the problem is based on the solutions from the subproblems. v = {27.962141608, -53.643959788}
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