x^4+3x^2=8

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Solution for x^4+3x^2=8 equation:


Simplifying
x4 + 3x2 = 8

Reorder the terms:
3x2 + x4 = 8

Solving
3x2 + x4 = 8

Solving for variable 'x'.

Reorder the terms:
-8 + 3x2 + x4 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 3x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 3x2 + 8 + x4 = 0 + 8

Reorder the terms:
-8 + 8 + 3x2 + x4 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 3x2 + x4 = 0 + 8
3x2 + x4 = 0 + 8

Combine like terms: 0 + 8 = 8
3x2 + x4 = 8

The x term is 3x2.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x2 + 2.25 + x4 = 8 + 2.25

Reorder the terms:
2.25 + 3x2 + x4 = 8 + 2.25

Combine like terms: 8 + 2.25 = 10.25
2.25 + 3x2 + x4 = 10.25

Factor a perfect square on the left side:
(x2 + 1.5)(x2 + 1.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x2 + 1.5) equal to 3.201562119 and -3.201562119.

Subproblem 1

x2 + 1.5 = 3.201562119 Simplifying x2 + 1.5 = 3.201562119 Reorder the terms: 1.5 + x2 = 3.201562119 Solving 1.5 + x2 = 3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x2 = 3.201562119 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = 3.201562119 + -1.5 x2 = 3.201562119 + -1.5 Combine like terms: 3.201562119 + -1.5 = 1.701562119 x2 = 1.701562119 Simplifying x2 = 1.701562119 Take the square root of each side: x = {-1.304439389, 1.304439389}

Subproblem 2

x2 + 1.5 = -3.201562119 Simplifying x2 + 1.5 = -3.201562119 Reorder the terms: 1.5 + x2 = -3.201562119 Solving 1.5 + x2 = -3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x2 = -3.201562119 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = -3.201562119 + -1.5 x2 = -3.201562119 + -1.5 Combine like terms: -3.201562119 + -1.5 = -4.701562119 x2 = -4.701562119 Simplifying x2 = -4.701562119 Reorder the terms: 4.701562119 + x2 = -4.701562119 + 4.701562119 Combine like terms: -4.701562119 + 4.701562119 = 0.000000000 4.701562119 + 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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