c^2(c^2-5)=2c^2-11

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Solution for c^2(c^2-5)=2c^2-11 equation: 


Simplifying
c2(c2 + -5) = 2c2 + -11

Reorder the terms:
c2(-5 + c2) = 2c2 + -11
(-5 * c2 + c2 * c2) = 2c2 + -11
(-5c2 + c4) = 2c2 + -11

Reorder the terms:
-5c2 + c4 = -11 + 2c2

Solving
-5c2 + c4 = -11 + 2c2

Solving for variable 'c'.

Reorder the terms:
11 + -5c2 + -2c2 + c4 = -11 + 2c2 + 11 + -2c2

Combine like terms: -5c2 + -2c2 = -7c2
11 + -7c2 + c4 = -11 + 2c2 + 11 + -2c2

Reorder the terms:
11 + -7c2 + c4 = -11 + 11 + 2c2 + -2c2

Combine like terms: -11 + 11 = 0
11 + -7c2 + c4 = 0 + 2c2 + -2c2
11 + -7c2 + c4 = 2c2 + -2c2

Combine like terms: 2c2 + -2c2 = 0
11 + -7c2 + c4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -7c2 + -11 + c4 = 0 + -11

Reorder the terms:
11 + -11 + -7c2 + c4 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -7c2 + c4 = 0 + -11
-7c2 + c4 = 0 + -11

Combine like terms: 0 + -11 = -11
-7c2 + c4 = -11

The c term is -7c2.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7c2 + 12.25 + c4 = -11 + 12.25

Reorder the terms:
12.25 + -7c2 + c4 = -11 + 12.25

Combine like terms: -11 + 12.25 = 1.25
12.25 + -7c2 + c4 = 1.25

Factor a perfect square on the left side:
(c2 + -3.5)(c2 + -3.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(c2 + -3.5) equal to 1.118033989 and -1.118033989.


Subproblem 1
c2 + -3.5 = 1.118033989

Simplifying
c2 + -3.5 = 1.118033989

Reorder the terms:
-3.5 + c2 = 1.118033989

Solving
-3.5 + c2 = 1.118033989

Solving for variable 'c'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + c2 = 1.118033989 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + c2 = 1.118033989 + 3.5
c2 = 1.118033989 + 3.5

Combine like terms: 1.118033989 + 3.5 = 4.618033989
c2 = 4.618033989

Simplifying
c2 = 4.618033989

Take the square root of each side:
c = {-2.148961142, 2.148961142}


Subproblem 2
c2 + -3.5 = -1.118033989

Simplifying
c2 + -3.5 = -1.118033989

Reorder the terms:
-3.5 + c2 = -1.118033989

Solving
-3.5 + c2 = -1.118033989

Solving for variable 'c'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + c2 = -1.118033989 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + c2 = -1.118033989 + 3.5
c2 = -1.118033989 + 3.5

Combine like terms: -1.118033989 + 3.5 = 2.381966011
c2 = 2.381966011

Simplifying
c2 = 2.381966011

Take the square root of each side:
c = {-1.543361918, 1.543361918}


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {-2.148961142, 2.148961142, -1.543361918, 1.543361918}

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