9x^4+15x^2-1=0

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Solution for 9x^4+15x^2-1=0 equation:


Simplifying
9x4 + 15x2 + -1 = 0

Reorder the terms:
-1 + 15x2 + 9x4 = 0

Solving
-1 + 15x2 + 9x4 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-0.1111111111 + 1.666666667x2 + x4 = 0

Move the constant term to the right:

Add '0.1111111111' to each side of the equation.
-0.1111111111 + 1.666666667x2 + 0.1111111111 + x4 = 0 + 0.1111111111

Reorder the terms:
-0.1111111111 + 0.1111111111 + 1.666666667x2 + x4 = 0 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + 1.666666667x2 + x4 = 0 + 0.1111111111
1.666666667x2 + x4 = 0 + 0.1111111111

Combine like terms: 0 + 0.1111111111 = 0.1111111111
1.666666667x2 + x4 = 0.1111111111

The x term is 1.666666667x2.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x2 + 0.6944444447 + x4 = 0.1111111111 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x2 + x4 = 0.1111111111 + 0.6944444447

Combine like terms: 0.1111111111 + 0.6944444447 = 0.8055555558
0.6944444447 + 1.666666667x2 + x4 = 0.8055555558

Factor a perfect square on the left side:
(x2 + 0.8333333335)(x2 + 0.8333333335) = 0.8055555558

Calculate the square root of the right side: 0.897527468

Break this problem into two subproblems by setting 
(x2 + 0.8333333335) equal to 0.897527468 and -0.897527468.

Subproblem 1

x2 + 0.8333333335 = 0.897527468 Simplifying x2 + 0.8333333335 = 0.897527468 Reorder the terms: 0.8333333335 + x2 = 0.897527468 Solving 0.8333333335 + x2 = 0.897527468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x2 = 0.897527468 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x2 = 0.897527468 + -0.8333333335 x2 = 0.897527468 + -0.8333333335 Combine like terms: 0.897527468 + -0.8333333335 = 0.0641941345 x2 = 0.0641941345 Simplifying x2 = 0.0641941345 Take the square root of each side: x = {-0.253365614, 0.253365614}

Subproblem 2

x2 + 0.8333333335 = -0.897527468 Simplifying x2 + 0.8333333335 = -0.897527468 Reorder the terms: 0.8333333335 + x2 = -0.897527468 Solving 0.8333333335 + x2 = -0.897527468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x2 = -0.897527468 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x2 = -0.897527468 + -0.8333333335 x2 = -0.897527468 + -0.8333333335 Combine like terms: -0.897527468 + -0.8333333335 = -1.7308608015 x2 = -1.7308608015 Simplifying x2 = -1.7308608015 Reorder the terms: 1.7308608015 + x2 = -1.7308608015 + 1.7308608015 Combine like terms: -1.7308608015 + 1.7308608015 = 0.0000000000 1.7308608015 + x2 = 0.0000000000 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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