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

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


Simplifying
-4x4 + 4x2 + 21 = 0

Reorder the terms:
21 + 4x2 + -4x4 = 0

Solving
21 + 4x2 + -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'.
-5.25 + -1x2 + x4 = 0

Move the constant term to the right:

Add '5.25' to each side of the equation.
-5.25 + -1x2 + 5.25 + x4 = 0 + 5.25

Reorder the terms:
-5.25 + 5.25 + -1x2 + x4 = 0 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + -1x2 + x4 = 0 + 5.25
-1x2 + x4 = 0 + 5.25

Combine like terms: 0 + 5.25 = 5.25
-1x2 + x4 = 5.25

The x term is -1x2.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x2 + 0.25 + x4 = 5.25 + 0.25

Reorder the terms:
0.25 + -1x2 + x4 = 5.25 + 0.25

Combine like terms: 5.25 + 0.25 = 5.5
0.25 + -1x2 + x4 = 5.5

Factor a perfect square on the left side:
(x2 + -0.5)(x2 + -0.5) = 5.5

Calculate the square root of the right side: 2.34520788

Break this problem into two subproblems by setting 
(x2 + -0.5) equal to 2.34520788 and -2.34520788.

Subproblem 1

x2 + -0.5 = 2.34520788 Simplifying x2 + -0.5 = 2.34520788 Reorder the terms: -0.5 + x2 = 2.34520788 Solving -0.5 + x2 = 2.34520788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = 2.34520788 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = 2.34520788 + 0.5 x2 = 2.34520788 + 0.5 Combine like terms: 2.34520788 + 0.5 = 2.84520788 x2 = 2.84520788 Simplifying x2 = 2.84520788 Take the square root of each side: x = {-1.686774401, 1.686774401}

Subproblem 2

x2 + -0.5 = -2.34520788 Simplifying x2 + -0.5 = -2.34520788 Reorder the terms: -0.5 + x2 = -2.34520788 Solving -0.5 + x2 = -2.34520788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = -2.34520788 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = -2.34520788 + 0.5 x2 = -2.34520788 + 0.5 Combine like terms: -2.34520788 + 0.5 = -1.84520788 x2 = -1.84520788 Simplifying x2 = -1.84520788 Reorder the terms: 1.84520788 + x2 = -1.84520788 + 1.84520788 Combine like terms: -1.84520788 + 1.84520788 = 0.00000000 1.84520788 + 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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