5x^4+9x^2-23=0

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Solution for 5x^4+9x^2-23=0 equation:


Simplifying
5x4 + 9x2 + -23 = 0

Reorder the terms:
-23 + 9x2 + 5x4 = 0

Solving
-23 + 9x2 + 5x4 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-4.6 + 1.8x2 + x4 = 0

Move the constant term to the right:

Add '4.6' to each side of the equation.
-4.6 + 1.8x2 + 4.6 + x4 = 0 + 4.6

Reorder the terms:
-4.6 + 4.6 + 1.8x2 + x4 = 0 + 4.6

Combine like terms: -4.6 + 4.6 = 0.0
0.0 + 1.8x2 + x4 = 0 + 4.6
1.8x2 + x4 = 0 + 4.6

Combine like terms: 0 + 4.6 = 4.6
1.8x2 + x4 = 4.6

The x term is 1.8x2.  Take half its coefficient (0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
1.8x2 + 0.81 + x4 = 4.6 + 0.81

Reorder the terms:
0.81 + 1.8x2 + x4 = 4.6 + 0.81

Combine like terms: 4.6 + 0.81 = 5.41
0.81 + 1.8x2 + x4 = 5.41

Factor a perfect square on the left side:
(x2 + 0.9)(x2 + 0.9) = 5.41

Calculate the square root of the right side: 2.32594067

Break this problem into two subproblems by setting 
(x2 + 0.9) equal to 2.32594067 and -2.32594067.

Subproblem 1

x2 + 0.9 = 2.32594067 Simplifying x2 + 0.9 = 2.32594067 Reorder the terms: 0.9 + x2 = 2.32594067 Solving 0.9 + x2 = 2.32594067 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x2 = 2.32594067 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x2 = 2.32594067 + -0.9 x2 = 2.32594067 + -0.9 Combine like terms: 2.32594067 + -0.9 = 1.42594067 x2 = 1.42594067 Simplifying x2 = 1.42594067 Take the square root of each side: x = {-1.194127577, 1.194127577}

Subproblem 2

x2 + 0.9 = -2.32594067 Simplifying x2 + 0.9 = -2.32594067 Reorder the terms: 0.9 + x2 = -2.32594067 Solving 0.9 + x2 = -2.32594067 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x2 = -2.32594067 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x2 = -2.32594067 + -0.9 x2 = -2.32594067 + -0.9 Combine like terms: -2.32594067 + -0.9 = -3.22594067 x2 = -3.22594067 Simplifying x2 = -3.22594067 Reorder the terms: 3.22594067 + x2 = -3.22594067 + 3.22594067 Combine like terms: -3.22594067 + 3.22594067 = 0.00000000 3.22594067 + x2 = 0.00000000 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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