f(225f+3.50)-150=2000

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Solution for f(225f+3.50)-150=2000 equation:


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 = 3.08343817222

Subproblem 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 = -3.09899372778

Solution

The solution to the problem is based on the solutions from the subproblems. f = {3.08343817222, -3.09899372778}

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