3F+-6F-7F+10F^2-8=

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Solution for 3F+-6F-7F+10F^2-8= equation: 


Simplifying
3F + -6F + -7F + 10F2 + -8 = 0

Reorder the terms:
-8 + 3F + -6F + -7F + 10F2 = 0

Combine like terms: 3F + -6F = -3F
-8 + -3F + -7F + 10F2 = 0

Combine like terms: -3F + -7F = -10F
-8 + -10F + 10F2 = 0

Solving
-8 + -10F + 10F2 = 0

Solving for variable 'F'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -5F + 5F2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -5F + 5F2)' equal to zero and attempt to solve:

Simplifying
-4 + -5F + 5F2 = 0

Solving
-4 + -5F + 5F2 = 0

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

Divide each side by '5'.
-0.8 + -1F + F2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + -1F + 0.8 + F2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + -1F + F2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + -1F + F2 = 0 + 0.8
-1F + F2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
-1F + F2 = 0.8

The F term is -1F.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1F + 0.25 + F2 = 0.8 + 0.25

Reorder the terms:
0.25 + -1F + F2 = 0.8 + 0.25

Combine like terms: 0.8 + 0.25 = 1.05
0.25 + -1F + F2 = 1.05

Factor a perfect square on the left side:
(F + -0.5)(F + -0.5) = 1.05

Calculate the square root of the right side: 1.024695077

Break this problem into two subproblems by setting 
(F + -0.5) equal to 1.024695077 and -1.024695077.


Subproblem 1
F + -0.5 = 1.024695077

Simplifying
F + -0.5 = 1.024695077

Reorder the terms:
-0.5 + F = 1.024695077

Solving
-0.5 + F = 1.024695077

Solving for variable 'F'.

Move all terms containing F to the left, all other terms to the right.

Add '0.5' to each side of the equation.
-0.5 + 0.5 + F = 1.024695077 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + F = 1.024695077 + 0.5
F = 1.024695077 + 0.5

Combine like terms: 1.024695077 + 0.5 = 1.524695077
F = 1.524695077

Simplifying
F = 1.524695077


Subproblem 2
F + -0.5 = -1.024695077

Simplifying
F + -0.5 = -1.024695077

Reorder the terms:
-0.5 + F = -1.024695077

Solving
-0.5 + F = -1.024695077

Solving for variable 'F'.

Move all terms containing F to the left, all other terms to the right.

Add '0.5' to each side of the equation.
-0.5 + 0.5 + F = -1.024695077 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + F = -1.024695077 + 0.5
F = -1.024695077 + 0.5

Combine like terms: -1.024695077 + 0.5 = -0.524695077
F = -0.524695077

Simplifying
F = -0.524695077


Solution
The solution to the problem is based on the solutions
from the subproblems.
F = {1.524695077, -0.524695077}
Solution
F = {1.524695077, -0.524695077}

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