0.1x^4-2.4x^2-3.6=0

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Solution for 0.1x^4-2.4x^2-3.6=0 equation: 


Simplifying
0.1x4 + -2.4x2 + -3.6 = 0

Reorder the terms:
-3.6 + -2.4x2 + 0.1x4 = 0

Solving
-3.6 + -2.4x2 + 0.1x4 = 0

Solving for variable 'x'.

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

Divide each side by '0.1'.
-36 + -24x2 + x4 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -24x2 + 36 + x4 = 0 + 36

Reorder the terms:
-36 + 36 + -24x2 + x4 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -24x2 + x4 = 0 + 36
-24x2 + x4 = 0 + 36

Combine like terms: 0 + 36 = 36
-24x2 + x4 = 36

The x term is -24x2.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x2 + 144 + x4 = 36 + 144

Reorder the terms:
144 + -24x2 + x4 = 36 + 144

Combine like terms: 36 + 144 = 180
144 + -24x2 + x4 = 180

Factor a perfect square on the left side:
(x2 + -12)(x2 + -12) = 180

Calculate the square root of the right side: 13.416407865

Break this problem into two subproblems by setting 
(x2 + -12) equal to 13.416407865 and -13.416407865.


Subproblem 1
x2 + -12 = 13.416407865

Simplifying
x2 + -12 = 13.416407865

Reorder the terms:
-12 + x2 = 13.416407865

Solving
-12 + x2 = 13.416407865

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x2 = 13.416407865 + 12

Combine like terms: -12 + 12 = 0
0 + x2 = 13.416407865 + 12
x2 = 13.416407865 + 12

Combine like terms: 13.416407865 + 12 = 25.416407865
x2 = 25.416407865

Simplifying
x2 = 25.416407865

Take the square root of each side:
x = {-5.04146882, 5.04146882}


Subproblem 2
x2 + -12 = -13.416407865

Simplifying
x2 + -12 = -13.416407865

Reorder the terms:
-12 + x2 = -13.416407865

Solving
-12 + x2 = -13.416407865

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x2 = -13.416407865 + 12

Combine like terms: -12 + 12 = 0
0 + x2 = -13.416407865 + 12
x2 = -13.416407865 + 12

Combine like terms: -13.416407865 + 12 = -1.416407865
x2 = -1.416407865

Simplifying
x2 = -1.416407865

Reorder the terms:
1.416407865 + x2 = -1.416407865 + 1.416407865

Combine like terms: -1.416407865 + 1.416407865 = 0.000000000
1.416407865 + 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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