-3f^2+4f-3+8f^2+7f+1=

Solution for -3f^2+4f-3+8f^2+7f+1= equation:

Simplifying
-3f2 + 4f + -3 + 8f2 + 7f + 1 = 0

Reorder the terms:
-3 + 1 + 4f + 7f + -3f2 + 8f2 = 0

Combine like terms: -3 + 1 = -2
-2 + 4f + 7f + -3f2 + 8f2 = 0

Combine like terms: 4f + 7f = 11f
-2 + 11f + -3f2 + 8f2 = 0

Combine like terms: -3f2 + 8f2 = 5f2
-2 + 11f + 5f2 = 0

Solving
-2 + 11f + 5f2 = 0

Solving for variable 'f'.

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

Divide each side by '5'.
-0.4 + 2.2f + f2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 2.2f + 0.4 + f2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 2.2f + f2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 2.2f + f2 = 0 + 0.4
2.2f + f2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
2.2f + f2 = 0.4

The f term is 2.2f.  Take half its coefficient (1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
2.2f + 1.21 + f2 = 0.4 + 1.21

Reorder the terms:
1.21 + 2.2f + f2 = 0.4 + 1.21

Combine like terms: 0.4 + 1.21 = 1.61
1.21 + 2.2f + f2 = 1.61

Factor a perfect square on the left side:
(f + 1.1)(f + 1.1) = 1.61

Calculate the square root of the right side: 1.268857754

Break this problem into two subproblems by setting 
(f + 1.1) equal to 1.268857754 and -1.268857754.

Subproblem 1
f + 1.1 = 1.268857754

Simplifying
f + 1.1 = 1.268857754

Reorder the terms:
1.1 + f = 1.268857754

Solving
1.1 + f = 1.268857754

Solving for variable 'f'.

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

Add '-1.1' to each side of the equation.
1.1 + -1.1 + f = 1.268857754 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + f = 1.268857754 + -1.1
f = 1.268857754 + -1.1

Combine like terms: 1.268857754 + -1.1 = 0.168857754
f = 0.168857754

Simplifying
f = 0.168857754

Subproblem 2
f + 1.1 = -1.268857754

Simplifying
f + 1.1 = -1.268857754

Reorder the terms:
1.1 + f = -1.268857754

Solving
1.1 + f = -1.268857754

Solving for variable 'f'.

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

Add '-1.1' to each side of the equation.
1.1 + -1.1 + f = -1.268857754 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + f = -1.268857754 + -1.1
f = -1.268857754 + -1.1

Combine like terms: -1.268857754 + -1.1 = -2.368857754
f = -2.368857754

Simplifying
f = -2.368857754

Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {0.168857754, -2.368857754}