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Simplifying f(225f + 3.50) + -150 = 2000 Reorder the terms: f(3.50 + 225f) + -150 = 2000 (3.50 * f + 225f * f) + -150 = 2000 (3.50f + 225f2) + -150 = 2000 Reorder the terms: -150 + 3.50f + 225f2 = 2000 Solving -150 + 3.50f + 225f2 = 2000 Solving for variable 'f'. Reorder the terms: -150 + -2000 + 3.50f + 225f2 = 2000 + -2000 Combine like terms: -150 + -2000 = -2150 -2150 + 3.50f + 225f2 = 2000 + -2000 Combine like terms: 2000 + -2000 = 0 -2150 + 3.50f + 225f2 = 0 Begin completing the square. Divide all terms by 225 the coefficient of the squared term: Divide each side by '225'. -9.555555556 + 0.01555555556f + f2 = 0 Move the constant term to the right: Add '9.555555556' to each side of the equation. -9.555555556 + 0.01555555556f + 9.555555556 + f2 = 0 + 9.555555556 Reorder the terms: -9.555555556 + 9.555555556 + 0.01555555556f + f2 = 0 + 9.555555556 Combine like terms: -9.555555556 + 9.555555556 = 0.000000000 0.000000000 + 0.01555555556f + f2 = 0 + 9.555555556 0.01555555556f + f2 = 0 + 9.555555556 Combine like terms: 0 + 9.555555556 = 9.555555556 0.01555555556f + f2 = 9.555555556 The f term is 0.01555555556f. Take half its coefficient (0.00777777778). Square it (0.00006049382720) and add it to both sides. Add '0.00006049382720' to each side of the equation. 0.01555555556f + 0.00006049382720 + f2 = 9.555555556 + 0.00006049382720 Reorder the terms: 0.00006049382720 + 0.01555555556f + f2 = 9.555555556 + 0.00006049382720 Combine like terms: 9.555555556 + 0.00006049382720 = 9.5556160498272 0.00006049382720 + 0.01555555556f + f2 = 9.5556160498272 Factor a perfect square on the left side: (f + 0.00777777778)(f + 0.00777777778) = 9.5556160498272 Calculate the square root of the right side: 3.09121595 Break this problem into two subproblems by setting (f + 0.00777777778) equal to 3.09121595 and -3.09121595.Subproblem 1
f + 0.00777777778 = 3.09121595 Simplifying f + 0.00777777778 = 3.09121595 Reorder the terms: 0.00777777778 + f = 3.09121595 Solving 0.00777777778 + f = 3.09121595 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-0.00777777778' to each side of the equation. 0.00777777778 + -0.00777777778 + f = 3.09121595 + -0.00777777778 Combine like terms: 0.00777777778 + -0.00777777778 = 0.00000000000 0.00000000000 + f = 3.09121595 + -0.00777777778 f = 3.09121595 + -0.00777777778 Combine like terms: 3.09121595 + -0.00777777778 = 3.08343817222 f = 3.08343817222 Simplifying f = 3.08343817222Subproblem 2
f + 0.00777777778 = -3.09121595 Simplifying f + 0.00777777778 = -3.09121595 Reorder the terms: 0.00777777778 + f = -3.09121595 Solving 0.00777777778 + f = -3.09121595 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-0.00777777778' to each side of the equation. 0.00777777778 + -0.00777777778 + f = -3.09121595 + -0.00777777778 Combine like terms: 0.00777777778 + -0.00777777778 = 0.00000000000 0.00000000000 + f = -3.09121595 + -0.00777777778 f = -3.09121595 + -0.00777777778 Combine like terms: -3.09121595 + -0.00777777778 = -3.09899372778 f = -3.09899372778 Simplifying f = -3.09899372778Solution
The solution to the problem is based on the solutions from the subproblems. f = {3.08343817222, -3.09899372778}
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