x^4+3x^2-21=0

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Solution for x^4+3x^2-21=0 equation:


Simplifying
x4 + 3x2 + -21 = 0

Reorder the terms:
-21 + 3x2 + x4 = 0

Solving
-21 + 3x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 3x2 + 21 + x4 = 0 + 21

Reorder the terms:
-21 + 21 + 3x2 + x4 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 3x2 + x4 = 0 + 21
3x2 + x4 = 0 + 21

Combine like terms: 0 + 21 = 21
3x2 + x4 = 21

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 = 21 + 2.25

Reorder the terms:
2.25 + 3x2 + x4 = 21 + 2.25

Combine like terms: 21 + 2.25 = 23.25
2.25 + 3x2 + x4 = 23.25

Factor a perfect square on the left side:
(x2 + 1.5)(x2 + 1.5) = 23.25

Calculate the square root of the right side: 4.82182538

Break this problem into two subproblems by setting 
(x2 + 1.5) equal to 4.82182538 and -4.82182538.

Subproblem 1

x2 + 1.5 = 4.82182538 Simplifying x2 + 1.5 = 4.82182538 Reorder the terms: 1.5 + x2 = 4.82182538 Solving 1.5 + x2 = 4.82182538 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 = 4.82182538 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = 4.82182538 + -1.5 x2 = 4.82182538 + -1.5 Combine like terms: 4.82182538 + -1.5 = 3.32182538 x2 = 3.32182538 Simplifying x2 = 3.32182538 Take the square root of each side: x = {-1.822587551, 1.822587551}

Subproblem 2

x2 + 1.5 = -4.82182538 Simplifying x2 + 1.5 = -4.82182538 Reorder the terms: 1.5 + x2 = -4.82182538 Solving 1.5 + x2 = -4.82182538 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 = -4.82182538 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = -4.82182538 + -1.5 x2 = -4.82182538 + -1.5 Combine like terms: -4.82182538 + -1.5 = -6.32182538 x2 = -6.32182538 Simplifying x2 = -6.32182538 Reorder the terms: 6.32182538 + x2 = -6.32182538 + 6.32182538 Combine like terms: -6.32182538 + 6.32182538 = 0.00000000 6.32182538 + 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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