(5(x^4))+(24(x^2))+9=0

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Solution for (5(x^4))+(24(x^2))+9=0 equation: 


Simplifying
(5(x4)) + (24(x2)) + 9 = 0

Reorder the terms:
9 + (24x2) + (5x4) = 0

Solving
9 + (24x2) + (5x4) = 0

Solving for variable 'x'.

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

Divide each side by '5'.
1.8 + (4.8x2) + x4 = 0

Move the constant term to the right:

Add '-1.8' to each side of the equation.
1.8 + (4.8x2) + -1.8 + x4 = 0 + -1.8

Reorder the terms:
1.8 + -1.8 + (4.8x2) + x4 = 0 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + (4.8x2) + x4 = 0 + -1.8
(4.8x2) + x4 = 0 + -1.8

Combine like terms: 0 + -1.8 = -1.8
(4.8x2) + x4 = -1.8

The x term is (4.8x2).  Take half its coefficient (2.4).
Square it (5.76) and add it to both sides.

Add '5.76' to each side of the equation.
(4.8x2) + 5.76 + x4 = -1.8 + 5.76

Reorder the terms:
5.76 + (4.8x2) + x4 = -1.8 + 5.76

Combine like terms: -1.8 + 5.76 = 3.96
5.76 + (4.8x2) + x4 = 3.96

Factor a perfect square on the left side:
((x2) + 2.4)((x2) + 2.4) = 3.96

Calculate the square root of the right side: 1.989974874

Break this problem into two subproblems by setting 
((x2) + 2.4) equal to 1.989974874 and -1.989974874.


Subproblem 1
(x2) + 2.4 = 1.989974874

Simplifying
(x2) + 2.4 = 1.989974874
x2 + 2.4 = 1.989974874

Reorder the terms:
2.4 + x2 = 1.989974874

Solving
2.4 + x2 = 1.989974874

Solving for variable 'x'.

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

Add '-2.4' to each side of the equation.
2.4 + -2.4 + x2 = 1.989974874 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + x2 = 1.989974874 + -2.4
x2 = 1.989974874 + -2.4

Combine like terms: 1.989974874 + -2.4 = -0.410025126
x2 = -0.410025126

Simplifying
x2 = -0.410025126

Reorder the terms:
0.410025126 + x2 = -0.410025126 + 0.410025126

Combine like terms: -0.410025126 + 0.410025126 = 0.000000000
0.410025126 + x2 = 0.000000000

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


Subproblem 2
(x2) + 2.4 = -1.989974874

Simplifying
(x2) + 2.4 = -1.989974874
x2 + 2.4 = -1.989974874

Reorder the terms:
2.4 + x2 = -1.989974874

Solving
2.4 + x2 = -1.989974874

Solving for variable 'x'.

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

Add '-2.4' to each side of the equation.
2.4 + -2.4 + x2 = -1.989974874 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + x2 = -1.989974874 + -2.4
x2 = -1.989974874 + -2.4

Combine like terms: -1.989974874 + -2.4 = -4.389974874
x2 = -4.389974874

Simplifying
x2 = -4.389974874

Reorder the terms:
4.389974874 + x2 = -4.389974874 + 4.389974874

Combine like terms: -4.389974874 + 4.389974874 = 0.000000000
4.389974874 + 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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