w^2(w^2-4)=3w^2-4

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Solution for w^2(w^2-4)=3w^2-4 equation: 


Simplifying
w2(w2 + -4) = 3w2 + -4

Reorder the terms:
w2(-4 + w2) = 3w2 + -4
(-4 * w2 + w2 * w2) = 3w2 + -4
(-4w2 + w4) = 3w2 + -4

Reorder the terms:
-4w2 + w4 = -4 + 3w2

Solving
-4w2 + w4 = -4 + 3w2

Solving for variable 'w'.

Reorder the terms:
4 + -4w2 + -3w2 + w4 = -4 + 3w2 + 4 + -3w2

Combine like terms: -4w2 + -3w2 = -7w2
4 + -7w2 + w4 = -4 + 3w2 + 4 + -3w2

Reorder the terms:
4 + -7w2 + w4 = -4 + 4 + 3w2 + -3w2

Combine like terms: -4 + 4 = 0
4 + -7w2 + w4 = 0 + 3w2 + -3w2
4 + -7w2 + w4 = 3w2 + -3w2

Combine like terms: 3w2 + -3w2 = 0
4 + -7w2 + w4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -7w2 + -4 + w4 = 0 + -4

Reorder the terms:
4 + -4 + -7w2 + w4 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7w2 + w4 = 0 + -4
-7w2 + w4 = 0 + -4

Combine like terms: 0 + -4 = -4
-7w2 + w4 = -4

The w term is -7w2.  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.
-7w2 + 12.25 + w4 = -4 + 12.25

Reorder the terms:
12.25 + -7w2 + w4 = -4 + 12.25

Combine like terms: -4 + 12.25 = 8.25
12.25 + -7w2 + w4 = 8.25

Factor a perfect square on the left side:
(w2 + -3.5)(w2 + -3.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(w2 + -3.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
w2 + -3.5 = 2.872281323

Simplifying
w2 + -3.5 = 2.872281323

Reorder the terms:
-3.5 + w2 = 2.872281323

Solving
-3.5 + w2 = 2.872281323

Solving for variable 'w'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + w2 = 2.872281323 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + w2 = 2.872281323 + 3.5
w2 = 2.872281323 + 3.5

Combine like terms: 2.872281323 + 3.5 = 6.372281323
w2 = 6.372281323

Simplifying
w2 = 6.372281323

Take the square root of each side:
w = {-2.524337799, 2.524337799}


Subproblem 2
w2 + -3.5 = -2.872281323

Simplifying
w2 + -3.5 = -2.872281323

Reorder the terms:
-3.5 + w2 = -2.872281323

Solving
-3.5 + w2 = -2.872281323

Solving for variable 'w'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + w2 = -2.872281323 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + w2 = -2.872281323 + 3.5
w2 = -2.872281323 + 3.5

Combine like terms: -2.872281323 + 3.5 = 0.627718677
w2 = 0.627718677

Simplifying
w2 = 0.627718677

Take the square root of each side:
w = {-0.792286992, 0.792286992}


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-2.524337799, 2.524337799, -0.792286992, 0.792286992}

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