w^4-w^2-9=

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Solution for w^4-w^2-9= equation: 


Simplifying
w4 + -1w2 + -9 = 0

Reorder the terms:
-9 + -1w2 + w4 = 0

Solving
-9 + -1w2 + w4 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -1w2 + 9 + w4 = 0 + 9

Reorder the terms:
-9 + 9 + -1w2 + w4 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1w2 + w4 = 0 + 9
-1w2 + w4 = 0 + 9

Combine like terms: 0 + 9 = 9
-1w2 + w4 = 9

The w term is -1w2.  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.
-1w2 + 0.25 + w4 = 9 + 0.25

Reorder the terms:
0.25 + -1w2 + w4 = 9 + 0.25

Combine like terms: 9 + 0.25 = 9.25
0.25 + -1w2 + w4 = 9.25

Factor a perfect square on the left side:
(w2 + -0.5)(w2 + -0.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(w2 + -0.5) equal to 3.041381265 and -3.041381265.


Subproblem 1
w2 + -0.5 = 3.041381265

Simplifying
w2 + -0.5 = 3.041381265

Reorder the terms:
-0.5 + w2 = 3.041381265

Solving
-0.5 + w2 = 3.041381265

Solving for variable 'w'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + w2 = 3.041381265 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + w2 = 3.041381265 + 0.5
w2 = 3.041381265 + 0.5

Combine like terms: 3.041381265 + 0.5 = 3.541381265
w2 = 3.541381265

Simplifying
w2 = 3.541381265

Take the square root of each side:
w = {-1.881855803, 1.881855803}


Subproblem 2
w2 + -0.5 = -3.041381265

Simplifying
w2 + -0.5 = -3.041381265

Reorder the terms:
-0.5 + w2 = -3.041381265

Solving
-0.5 + w2 = -3.041381265

Solving for variable 'w'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + w2 = -3.041381265 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + w2 = -3.041381265 + 0.5
w2 = -3.041381265 + 0.5

Combine like terms: -3.041381265 + 0.5 = -2.541381265
w2 = -2.541381265

Simplifying
w2 = -2.541381265

Reorder the terms:
2.541381265 + w2 = -2.541381265 + 2.541381265

Combine like terms: -2.541381265 + 2.541381265 = 0.000000000
2.541381265 + w2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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