(x^4)+(7x^2)-36=0

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Solution for (x^4)+(7x^2)-36=0 equation: 


Simplifying
(x4) + (7x2) + -36 = 0
x4 + (7x2) + -36 = 0

Reorder the terms:
-36 + (7x2) + x4 = 0

Solving
-36 + (7x2) + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + (7x2) + 36 + x4 = 0 + 36

Reorder the terms:
-36 + 36 + (7x2) + x4 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + (7x2) + x4 = 0 + 36
(7x2) + x4 = 0 + 36

Combine like terms: 0 + 36 = 36
(7x2) + x4 = 36

The x term is (7x2).  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.
(7x2) + 12.25 + x4 = 36 + 12.25

Reorder the terms:
12.25 + (7x2) + x4 = 36 + 12.25

Combine like terms: 36 + 12.25 = 48.25
12.25 + (7x2) + x4 = 48.25

Factor a perfect square on the left side:
(x2 + 3.5)(x2 + 3.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(x2 + 3.5) equal to 6.946221995 and -6.946221995.


Subproblem 1
x2 + 3.5 = 6.946221995

Simplifying
x2 + 3.5 = 6.946221995

Reorder the terms:
3.5 + x2 = 6.946221995

Solving
3.5 + x2 = 6.946221995

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x2 = 6.946221995 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x2 = 6.946221995 + -3.5
x2 = 6.946221995 + -3.5

Combine like terms: 6.946221995 + -3.5 = 3.446221995
x2 = 3.446221995

Simplifying
x2 = 3.446221995

Take the square root of each side:
x = {-1.856400279, 1.856400279}


Subproblem 2
x2 + 3.5 = -6.946221995

Simplifying
x2 + 3.5 = -6.946221995

Reorder the terms:
3.5 + x2 = -6.946221995

Solving
3.5 + x2 = -6.946221995

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x2 = -6.946221995 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x2 = -6.946221995 + -3.5
x2 = -6.946221995 + -3.5

Combine like terms: -6.946221995 + -3.5 = -10.446221995
x2 = -10.446221995

Simplifying
x2 = -10.446221995

Reorder the terms:
10.446221995 + x2 = -10.446221995 + 10.446221995

Combine like terms: -10.446221995 + 10.446221995 = 0.000000000
10.446221995 + x2 = 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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