40x^4+36x^2-27=0

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Solution for 40x^4+36x^2-27=0 equation: 


Simplifying
40x4 + 36x2 + -27 = 0

Reorder the terms:
-27 + 36x2 + 40x4 = 0

Solving
-27 + 36x2 + 40x4 = 0

Solving for variable 'x'.

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

Divide each side by '40'.
-0.675 + 0.9x2 + x4 = 0

Move the constant term to the right:

Add '0.675' to each side of the equation.
-0.675 + 0.9x2 + 0.675 + x4 = 0 + 0.675

Reorder the terms:
-0.675 + 0.675 + 0.9x2 + x4 = 0 + 0.675

Combine like terms: -0.675 + 0.675 = 0.000
0.000 + 0.9x2 + x4 = 0 + 0.675
0.9x2 + x4 = 0 + 0.675

Combine like terms: 0 + 0.675 = 0.675
0.9x2 + x4 = 0.675

The x term is 0.9x2.  Take half its coefficient (0.45).
Square it (0.2025) and add it to both sides.

Add '0.2025' to each side of the equation.
0.9x2 + 0.2025 + x4 = 0.675 + 0.2025

Reorder the terms:
0.2025 + 0.9x2 + x4 = 0.675 + 0.2025

Combine like terms: 0.675 + 0.2025 = 0.8775
0.2025 + 0.9x2 + x4 = 0.8775

Factor a perfect square on the left side:
(x2 + 0.45)(x2 + 0.45) = 0.8775

Calculate the square root of the right side: 0.9367497

Break this problem into two subproblems by setting 
(x2 + 0.45) equal to 0.9367497 and -0.9367497.


Subproblem 1
x2 + 0.45 = 0.9367497

Simplifying
x2 + 0.45 = 0.9367497

Reorder the terms:
0.45 + x2 = 0.9367497

Solving
0.45 + x2 = 0.9367497

Solving for variable 'x'.

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

Add '-0.45' to each side of the equation.
0.45 + -0.45 + x2 = 0.9367497 + -0.45

Combine like terms: 0.45 + -0.45 = 0.00
0.00 + x2 = 0.9367497 + -0.45
x2 = 0.9367497 + -0.45

Combine like terms: 0.9367497 + -0.45 = 0.4867497
x2 = 0.4867497

Simplifying
x2 = 0.4867497

Take the square root of each side:
x = {-0.697674494, 0.697674494}


Subproblem 2
x2 + 0.45 = -0.9367497

Simplifying
x2 + 0.45 = -0.9367497

Reorder the terms:
0.45 + x2 = -0.9367497

Solving
0.45 + x2 = -0.9367497

Solving for variable 'x'.

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

Add '-0.45' to each side of the equation.
0.45 + -0.45 + x2 = -0.9367497 + -0.45

Combine like terms: 0.45 + -0.45 = 0.00
0.00 + x2 = -0.9367497 + -0.45
x2 = -0.9367497 + -0.45

Combine like terms: -0.9367497 + -0.45 = -1.3867497
x2 = -1.3867497

Simplifying
x2 = -1.3867497

Reorder the terms:
1.3867497 + x2 = -1.3867497 + 1.3867497

Combine like terms: -1.3867497 + 1.3867497 = 0.0000000
1.3867497 + x2 = 0.0000000

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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