4f(6f-8)=35

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Solution for 4f(6f-8)=35 equation:


Simplifying
4f(6f + -8) = 35

Reorder the terms:
4f(-8 + 6f) = 35
(-8 * 4f + 6f * 4f) = 35
(-32f + 24f2) = 35

Solving
-32f + 24f2 = 35

Solving for variable 'f'.

Reorder the terms:
-35 + -32f + 24f2 = 35 + -35

Combine like terms: 35 + -35 = 0
-35 + -32f + 24f2 = 0

Begin completing the square.  Divide all terms by
24 the coefficient of the squared term: 

Divide each side by '24'.
-1.458333333 + -1.333333333f + f2 = 0

Move the constant term to the right:

Add '1.458333333' to each side of the equation.
-1.458333333 + -1.333333333f + 1.458333333 + f2 = 0 + 1.458333333

Reorder the terms:
-1.458333333 + 1.458333333 + -1.333333333f + f2 = 0 + 1.458333333

Combine like terms: -1.458333333 + 1.458333333 = 0.000000000
0.000000000 + -1.333333333f + f2 = 0 + 1.458333333
-1.333333333f + f2 = 0 + 1.458333333

Combine like terms: 0 + 1.458333333 = 1.458333333
-1.333333333f + f2 = 1.458333333

The f term is -1.333333333f.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333f + 0.4444444442 + f2 = 1.458333333 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333f + f2 = 1.458333333 + 0.4444444442

Combine like terms: 1.458333333 + 0.4444444442 = 1.9027777772
0.4444444442 + -1.333333333f + f2 = 1.9027777772

Factor a perfect square on the left side:
(f + -0.6666666665)(f + -0.6666666665) = 1.9027777772

Calculate the square root of the right side: 1.379412113

Break this problem into two subproblems by setting 
(f + -0.6666666665) equal to 1.379412113 and -1.379412113.

Subproblem 1

f + -0.6666666665 = 1.379412113 Simplifying f + -0.6666666665 = 1.379412113 Reorder the terms: -0.6666666665 + f = 1.379412113 Solving -0.6666666665 + f = 1.379412113 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + f = 1.379412113 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + f = 1.379412113 + 0.6666666665 f = 1.379412113 + 0.6666666665 Combine like terms: 1.379412113 + 0.6666666665 = 2.0460787795 f = 2.0460787795 Simplifying f = 2.0460787795

Subproblem 2

f + -0.6666666665 = -1.379412113 Simplifying f + -0.6666666665 = -1.379412113 Reorder the terms: -0.6666666665 + f = -1.379412113 Solving -0.6666666665 + f = -1.379412113 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + f = -1.379412113 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + f = -1.379412113 + 0.6666666665 f = -1.379412113 + 0.6666666665 Combine like terms: -1.379412113 + 0.6666666665 = -0.7127454465 f = -0.7127454465 Simplifying f = -0.7127454465

Solution

The solution to the problem is based on the solutions from the subproblems. f = {2.0460787795, -0.7127454465}

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