4x^4+10x^2+3=0

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Solution for 4x^4+10x^2+3=0 equation:


Simplifying
4x4 + 10x2 + 3 = 0

Reorder the terms:
3 + 10x2 + 4x4 = 0

Solving
3 + 10x2 + 4x4 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
0.75 + 2.5x2 + x4 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + 2.5x2 + -0.75 + x4 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + 2.5x2 + x4 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + 2.5x2 + x4 = 0 + -0.75
2.5x2 + x4 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
2.5x2 + x4 = -0.75

The x term is 2.5x2.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x2 + 1.5625 + x4 = -0.75 + 1.5625

Reorder the terms:
1.5625 + 2.5x2 + x4 = -0.75 + 1.5625

Combine like terms: -0.75 + 1.5625 = 0.8125
1.5625 + 2.5x2 + x4 = 0.8125

Factor a perfect square on the left side:
(x2 + 1.25)(x2 + 1.25) = 0.8125

Calculate the square root of the right side: 0.901387819

Break this problem into two subproblems by setting 
(x2 + 1.25) equal to 0.901387819 and -0.901387819.

Subproblem 1

x2 + 1.25 = 0.901387819 Simplifying x2 + 1.25 = 0.901387819 Reorder the terms: 1.25 + x2 = 0.901387819 Solving 1.25 + x2 = 0.901387819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x2 = 0.901387819 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x2 = 0.901387819 + -1.25 x2 = 0.901387819 + -1.25 Combine like terms: 0.901387819 + -1.25 = -0.348612181 x2 = -0.348612181 Simplifying x2 = -0.348612181 Reorder the terms: 0.348612181 + x2 = -0.348612181 + 0.348612181 Combine like terms: -0.348612181 + 0.348612181 = 0.000000000 0.348612181 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

Subproblem 2

x2 + 1.25 = -0.901387819 Simplifying x2 + 1.25 = -0.901387819 Reorder the terms: 1.25 + x2 = -0.901387819 Solving 1.25 + x2 = -0.901387819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x2 = -0.901387819 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x2 = -0.901387819 + -1.25 x2 = -0.901387819 + -1.25 Combine like terms: -0.901387819 + -1.25 = -2.151387819 x2 = -2.151387819 Simplifying x2 = -2.151387819 Reorder the terms: 2.151387819 + x2 = -2.151387819 + 2.151387819 Combine like terms: -2.151387819 + 2.151387819 = 0.000000000 2.151387819 + 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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