4x^4-15x^2-28=

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Solution for 4x^4-15x^2-28= equation: 


Simplifying
4x4 + -15x2 + -28 = 0

Reorder the terms:
-28 + -15x2 + 4x4 = 0

Solving
-28 + -15x2 + 4x4 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-7 + -3.75x2 + x4 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -3.75x2 + 7 + x4 = 0 + 7

Reorder the terms:
-7 + 7 + -3.75x2 + x4 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3.75x2 + x4 = 0 + 7
-3.75x2 + x4 = 0 + 7

Combine like terms: 0 + 7 = 7
-3.75x2 + x4 = 7

The x term is -3.75x2.  Take half its coefficient (-1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
-3.75x2 + 3.515625 + x4 = 7 + 3.515625

Reorder the terms:
3.515625 + -3.75x2 + x4 = 7 + 3.515625

Combine like terms: 7 + 3.515625 = 10.515625
3.515625 + -3.75x2 + x4 = 10.515625

Factor a perfect square on the left side:
(x2 + -1.875)(x2 + -1.875) = 10.515625

Calculate the square root of the right side: 3.242780443

Break this problem into two subproblems by setting 
(x2 + -1.875) equal to 3.242780443 and -3.242780443.


Subproblem 1
x2 + -1.875 = 3.242780443

Simplifying
x2 + -1.875 = 3.242780443

Reorder the terms:
-1.875 + x2 = 3.242780443

Solving
-1.875 + x2 = 3.242780443

Solving for variable 'x'.

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

Add '1.875' to each side of the equation.
-1.875 + 1.875 + x2 = 3.242780443 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + x2 = 3.242780443 + 1.875
x2 = 3.242780443 + 1.875

Combine like terms: 3.242780443 + 1.875 = 5.117780443
x2 = 5.117780443

Simplifying
x2 = 5.117780443

Take the square root of each side:
x = {-2.262251189, 2.262251189}


Subproblem 2
x2 + -1.875 = -3.242780443

Simplifying
x2 + -1.875 = -3.242780443

Reorder the terms:
-1.875 + x2 = -3.242780443

Solving
-1.875 + x2 = -3.242780443

Solving for variable 'x'.

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

Add '1.875' to each side of the equation.
-1.875 + 1.875 + x2 = -3.242780443 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + x2 = -3.242780443 + 1.875
x2 = -3.242780443 + 1.875

Combine like terms: -3.242780443 + 1.875 = -1.367780443
x2 = -1.367780443

Simplifying
x2 = -1.367780443

Reorder the terms:
1.367780443 + x2 = -1.367780443 + 1.367780443

Combine like terms: -1.367780443 + 1.367780443 = 0.000000000
1.367780443 + 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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