16x^4-7x^2-18=0

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Solution for 16x^4-7x^2-18=0 equation: 


Simplifying
16x4 + -7x2 + -18 = 0

Reorder the terms:
-18 + -7x2 + 16x4 = 0

Solving
-18 + -7x2 + 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'.
-1.125 + -0.4375x2 + x4 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + -0.4375x2 + 1.125 + x4 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + -0.4375x2 + x4 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + -0.4375x2 + x4 = 0 + 1.125
-0.4375x2 + x4 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
-0.4375x2 + x4 = 1.125

The x term is -0.4375x2.  Take half its coefficient (-0.21875).
Square it (0.0478515625) and add it to both sides.

Add '0.0478515625' to each side of the equation.
-0.4375x2 + 0.0478515625 + x4 = 1.125 + 0.0478515625

Reorder the terms:
0.0478515625 + -0.4375x2 + x4 = 1.125 + 0.0478515625

Combine like terms: 1.125 + 0.0478515625 = 1.1728515625
0.0478515625 + -0.4375x2 + x4 = 1.1728515625

Factor a perfect square on the left side:
(x2 + -0.21875)(x2 + -0.21875) = 1.1728515625

Calculate the square root of the right side: 1.082982716

Break this problem into two subproblems by setting 
(x2 + -0.21875) equal to 1.082982716 and -1.082982716.


Subproblem 1
x2 + -0.21875 = 1.082982716

Simplifying
x2 + -0.21875 = 1.082982716

Reorder the terms:
-0.21875 + x2 = 1.082982716

Solving
-0.21875 + x2 = 1.082982716

Solving for variable 'x'.

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

Add '0.21875' to each side of the equation.
-0.21875 + 0.21875 + x2 = 1.082982716 + 0.21875

Combine like terms: -0.21875 + 0.21875 = 0.00000
0.00000 + x2 = 1.082982716 + 0.21875
x2 = 1.082982716 + 0.21875

Combine like terms: 1.082982716 + 0.21875 = 1.301732716
x2 = 1.301732716

Simplifying
x2 = 1.301732716

Take the square root of each side:
x = {-1.140935018, 1.140935018}


Subproblem 2
x2 + -0.21875 = -1.082982716

Simplifying
x2 + -0.21875 = -1.082982716

Reorder the terms:
-0.21875 + x2 = -1.082982716

Solving
-0.21875 + x2 = -1.082982716

Solving for variable 'x'.

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

Add '0.21875' to each side of the equation.
-0.21875 + 0.21875 + x2 = -1.082982716 + 0.21875

Combine like terms: -0.21875 + 0.21875 = 0.00000
0.00000 + x2 = -1.082982716 + 0.21875
x2 = -1.082982716 + 0.21875

Combine like terms: -1.082982716 + 0.21875 = -0.864232716
x2 = -0.864232716

Simplifying
x2 = -0.864232716

Reorder the terms:
0.864232716 + x2 = -0.864232716 + 0.864232716

Combine like terms: -0.864232716 + 0.864232716 = 0.000000000
0.864232716 + 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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