10*x^4+20*x^2-1=0

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Solution for 10*x^4+20*x^2-1=0 equation:


Simplifying
10x4 + 20x2 + -1 = 0

Reorder the terms:
-1 + 20x2 + 10x4 = 0

Solving
-1 + 20x2 + 10x4 = 0

Solving for variable 'x'.

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

Divide each side by '10'.
-0.1 + 2x2 + x4 = 0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + 2x2 + 0.1 + x4 = 0 + 0.1

Reorder the terms:
-0.1 + 0.1 + 2x2 + x4 = 0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + 2x2 + x4 = 0 + 0.1
2x2 + x4 = 0 + 0.1

Combine like terms: 0 + 0.1 = 0.1
2x2 + x4 = 0.1

The x term is 2x2.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x2 + 1 + x4 = 0.1 + 1

Reorder the terms:
1 + 2x2 + x4 = 0.1 + 1

Combine like terms: 0.1 + 1 = 1.1
1 + 2x2 + x4 = 1.1

Factor a perfect square on the left side:
(x2 + 1)(x2 + 1) = 1.1

Calculate the square root of the right side: 1.048808848

Break this problem into two subproblems by setting 
(x2 + 1) equal to 1.048808848 and -1.048808848.

Subproblem 1

x2 + 1 = 1.048808848 Simplifying x2 + 1 = 1.048808848 Reorder the terms: 1 + x2 = 1.048808848 Solving 1 + x2 = 1.048808848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = 1.048808848 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 1.048808848 + -1 x2 = 1.048808848 + -1 Combine like terms: 1.048808848 + -1 = 0.048808848 x2 = 0.048808848 Simplifying x2 = 0.048808848 Take the square root of each side: x = {-0.220927246, 0.220927246}

Subproblem 2

x2 + 1 = -1.048808848 Simplifying x2 + 1 = -1.048808848 Reorder the terms: 1 + x2 = -1.048808848 Solving 1 + x2 = -1.048808848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = -1.048808848 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = -1.048808848 + -1 x2 = -1.048808848 + -1 Combine like terms: -1.048808848 + -1 = -2.048808848 x2 = -2.048808848 Simplifying x2 = -2.048808848 Reorder the terms: 2.048808848 + x2 = -2.048808848 + 2.048808848 Combine like terms: -2.048808848 + 2.048808848 = 0.000000000 2.048808848 + 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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