16x^4-14x^2-9=0

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Solution for 16x^4-14x^2-9=0 equation: 


Simplifying
16x4 + -14x2 + -9 = 0

Reorder the terms:
-9 + -14x2 + 16x4 = 0

Solving
-9 + -14x2 + 16x4 = 0

Solving for variable 'x'.

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

Divide each side by '16'.
-0.5625 + -0.875x2 + x4 = 0

Move the constant term to the right:

Add '0.5625' to each side of the equation.
-0.5625 + -0.875x2 + 0.5625 + x4 = 0 + 0.5625

Reorder the terms:
-0.5625 + 0.5625 + -0.875x2 + x4 = 0 + 0.5625

Combine like terms: -0.5625 + 0.5625 = 0.0000
0.0000 + -0.875x2 + x4 = 0 + 0.5625
-0.875x2 + x4 = 0 + 0.5625

Combine like terms: 0 + 0.5625 = 0.5625
-0.875x2 + x4 = 0.5625

The x term is -0.875x2.  Take half its coefficient (-0.4375).
Square it (0.19140625) and add it to both sides.

Add '0.19140625' to each side of the equation.
-0.875x2 + 0.19140625 + x4 = 0.5625 + 0.19140625

Reorder the terms:
0.19140625 + -0.875x2 + x4 = 0.5625 + 0.19140625

Combine like terms: 0.5625 + 0.19140625 = 0.75390625
0.19140625 + -0.875x2 + x4 = 0.75390625

Factor a perfect square on the left side:
(x2 + -0.4375)(x2 + -0.4375) = 0.75390625

Calculate the square root of the right side: 0.868277749

Break this problem into two subproblems by setting 
(x2 + -0.4375) equal to 0.868277749 and -0.868277749.


Subproblem 1
x2 + -0.4375 = 0.868277749

Simplifying
x2 + -0.4375 = 0.868277749

Reorder the terms:
-0.4375 + x2 = 0.868277749

Solving
-0.4375 + x2 = 0.868277749

Solving for variable 'x'.

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

Add '0.4375' to each side of the equation.
-0.4375 + 0.4375 + x2 = 0.868277749 + 0.4375

Combine like terms: -0.4375 + 0.4375 = 0.0000
0.0000 + x2 = 0.868277749 + 0.4375
x2 = 0.868277749 + 0.4375

Combine like terms: 0.868277749 + 0.4375 = 1.305777749
x2 = 1.305777749

Simplifying
x2 = 1.305777749

Take the square root of each side:
x = {-1.142706327, 1.142706327}


Subproblem 2
x2 + -0.4375 = -0.868277749

Simplifying
x2 + -0.4375 = -0.868277749

Reorder the terms:
-0.4375 + x2 = -0.868277749

Solving
-0.4375 + x2 = -0.868277749

Solving for variable 'x'.

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

Add '0.4375' to each side of the equation.
-0.4375 + 0.4375 + x2 = -0.868277749 + 0.4375

Combine like terms: -0.4375 + 0.4375 = 0.0000
0.0000 + x2 = -0.868277749 + 0.4375
x2 = -0.868277749 + 0.4375

Combine like terms: -0.868277749 + 0.4375 = -0.430777749
x2 = -0.430777749

Simplifying
x2 = -0.430777749

Reorder the terms:
0.430777749 + x2 = -0.430777749 + 0.430777749

Combine like terms: -0.430777749 + 0.430777749 = 0.000000000
0.430777749 + 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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