16.0x^4+15x^2-3.5=0

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Solution for 16.0x^4+15x^2-3.5=0 equation: 


Simplifying
16.0x4 + 15x2 + -3.5 = 0

Reorder the terms:
-3.5 + 15x2 + 16.0x4 = 0

Solving
-3.5 + 15x2 + 16.0x4 = 0

Solving for variable 'x'.

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

Divide each side by '16.0'.
-0.21875 + 0.9375x2 + x4 = 0

Move the constant term to the right:

Add '0.21875' to each side of the equation.
-0.21875 + 0.9375x2 + 0.21875 + x4 = 0 + 0.21875

Reorder the terms:
-0.21875 + 0.21875 + 0.9375x2 + x4 = 0 + 0.21875

Combine like terms: -0.21875 + 0.21875 = 0.00000
0.00000 + 0.9375x2 + x4 = 0 + 0.21875
0.9375x2 + x4 = 0 + 0.21875

Combine like terms: 0 + 0.21875 = 0.21875
0.9375x2 + x4 = 0.21875

The x term is 0.9375x2.  Take half its coefficient (0.46875).
Square it (0.2197265625) and add it to both sides.

Add '0.2197265625' to each side of the equation.
0.9375x2 + 0.2197265625 + x4 = 0.21875 + 0.2197265625

Reorder the terms:
0.2197265625 + 0.9375x2 + x4 = 0.21875 + 0.2197265625

Combine like terms: 0.21875 + 0.2197265625 = 0.4384765625
0.2197265625 + 0.9375x2 + x4 = 0.4384765625

Factor a perfect square on the left side:
(x2 + 0.46875)(x2 + 0.46875) = 0.4384765625

Calculate the square root of the right side: 0.662175628

Break this problem into two subproblems by setting 
(x2 + 0.46875) equal to 0.662175628 and -0.662175628.


Subproblem 1
x2 + 0.46875 = 0.662175628

Simplifying
x2 + 0.46875 = 0.662175628

Reorder the terms:
0.46875 + x2 = 0.662175628

Solving
0.46875 + x2 = 0.662175628

Solving for variable 'x'.

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

Add '-0.46875' to each side of the equation.
0.46875 + -0.46875 + x2 = 0.662175628 + -0.46875

Combine like terms: 0.46875 + -0.46875 = 0.00000
0.00000 + x2 = 0.662175628 + -0.46875
x2 = 0.662175628 + -0.46875

Combine like terms: 0.662175628 + -0.46875 = 0.193425628
x2 = 0.193425628

Simplifying
x2 = 0.193425628

Take the square root of each side:
x = {-0.439801805, 0.439801805}


Subproblem 2
x2 + 0.46875 = -0.662175628

Simplifying
x2 + 0.46875 = -0.662175628

Reorder the terms:
0.46875 + x2 = -0.662175628

Solving
0.46875 + x2 = -0.662175628

Solving for variable 'x'.

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

Add '-0.46875' to each side of the equation.
0.46875 + -0.46875 + x2 = -0.662175628 + -0.46875

Combine like terms: 0.46875 + -0.46875 = 0.00000
0.00000 + x2 = -0.662175628 + -0.46875
x2 = -0.662175628 + -0.46875

Combine like terms: -0.662175628 + -0.46875 = -1.130925628
x2 = -1.130925628

Simplifying
x2 = -1.130925628

Reorder the terms:
1.130925628 + x2 = -1.130925628 + 1.130925628

Combine like terms: -1.130925628 + 1.130925628 = 0.000000000
1.130925628 + 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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