x^4-3x^2=2

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Solution for x^4-3x^2=2 equation:


Simplifying
x4 + -3x2 = 2

Reorder the terms:
-3x2 + x4 = 2

Solving
-3x2 + x4 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + -3x2 + x4 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -3x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -3x2 + 2 + x4 = 0 + 2

Reorder the terms:
-2 + 2 + -3x2 + x4 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x2 + x4 = 0 + 2
-3x2 + x4 = 0 + 2

Combine like terms: 0 + 2 = 2
-3x2 + x4 = 2

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 = 2 + 2.25

Reorder the terms:
2.25 + -3x2 + x4 = 2 + 2.25

Combine like terms: 2 + 2.25 = 4.25
2.25 + -3x2 + x4 = 4.25

Factor a perfect square on the left side:
(x2 + -1.5)(x2 + -1.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x2 + -1.5) equal to 2.061552813 and -2.061552813.

Subproblem 1

x2 + -1.5 = 2.061552813 Simplifying x2 + -1.5 = 2.061552813 Reorder the terms: -1.5 + x2 = 2.061552813 Solving -1.5 + x2 = 2.061552813 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 = 2.061552813 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = 2.061552813 + 1.5 x2 = 2.061552813 + 1.5 Combine like terms: 2.061552813 + 1.5 = 3.561552813 x2 = 3.561552813 Simplifying x2 = 3.561552813 Take the square root of each side: x = {-1.887207676, 1.887207676}

Subproblem 2

x2 + -1.5 = -2.061552813 Simplifying x2 + -1.5 = -2.061552813 Reorder the terms: -1.5 + x2 = -2.061552813 Solving -1.5 + x2 = -2.061552813 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 = -2.061552813 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = -2.061552813 + 1.5 x2 = -2.061552813 + 1.5 Combine like terms: -2.061552813 + 1.5 = -0.561552813 x2 = -0.561552813 Simplifying x2 = -0.561552813 Reorder the terms: 0.561552813 + x2 = -0.561552813 + 0.561552813 Combine like terms: -0.561552813 + 0.561552813 = 0.000000000 0.561552813 + 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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