744=8w^2+w^4

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Solution for 744=8w^2+w^4 equation: 


Simplifying
744 = 8w2 + w4

Solving
744 = 8w2 + w4

Solving for variable 'w'.

Reorder the terms:
744 + -8w2 + -1w4 = 8w2 + -8w2 + w4 + -1w4

Combine like terms: 8w2 + -8w2 = 0
744 + -8w2 + -1w4 = 0 + w4 + -1w4
744 + -8w2 + -1w4 = w4 + -1w4

Combine like terms: w4 + -1w4 = 0
744 + -8w2 + -1w4 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-744 + 8w2 + w4 = 0

Move the constant term to the right:

Add '744' to each side of the equation.
-744 + 8w2 + 744 + w4 = 0 + 744

Reorder the terms:
-744 + 744 + 8w2 + w4 = 0 + 744

Combine like terms: -744 + 744 = 0
0 + 8w2 + w4 = 0 + 744
8w2 + w4 = 0 + 744

Combine like terms: 0 + 744 = 744
8w2 + w4 = 744

The w term is 8w2.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8w2 + 16 + w4 = 744 + 16

Reorder the terms:
16 + 8w2 + w4 = 744 + 16

Combine like terms: 744 + 16 = 760
16 + 8w2 + w4 = 760

Factor a perfect square on the left side:
(w2 + 4)(w2 + 4) = 760

Calculate the square root of the right side: 27.568097504

Break this problem into two subproblems by setting 
(w2 + 4) equal to 27.568097504 and -27.568097504.


Subproblem 1
w2 + 4 = 27.568097504

Simplifying
w2 + 4 = 27.568097504

Reorder the terms:
4 + w2 = 27.568097504

Solving
4 + w2 = 27.568097504

Solving for variable 'w'.

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

Add '-4' to each side of the equation.
4 + -4 + w2 = 27.568097504 + -4

Combine like terms: 4 + -4 = 0
0 + w2 = 27.568097504 + -4
w2 = 27.568097504 + -4

Combine like terms: 27.568097504 + -4 = 23.568097504
w2 = 23.568097504

Simplifying
w2 = 23.568097504

Take the square root of each side:
w = {-4.854698498, 4.854698498}


Subproblem 2
w2 + 4 = -27.568097504

Simplifying
w2 + 4 = -27.568097504

Reorder the terms:
4 + w2 = -27.568097504

Solving
4 + w2 = -27.568097504

Solving for variable 'w'.

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

Add '-4' to each side of the equation.
4 + -4 + w2 = -27.568097504 + -4

Combine like terms: 4 + -4 = 0
0 + w2 = -27.568097504 + -4
w2 = -27.568097504 + -4

Combine like terms: -27.568097504 + -4 = -31.568097504
w2 = -31.568097504

Simplifying
w2 = -31.568097504

Reorder the terms:
31.568097504 + w2 = -31.568097504 + 31.568097504

Combine like terms: -31.568097504 + 31.568097504 = 0.000000000
31.568097504 + 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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