24a^4-4a^2=1

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Solution for 24a^4-4a^2=1 equation:


Simplifying
24a4 + -4a2 = 1

Reorder the terms:
-4a2 + 24a4 = 1

Solving
-4a2 + 24a4 = 1

Solving for variable 'a'.

Reorder the terms:
-1 + -4a2 + 24a4 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -4a2 + 24a4 = 0

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

Divide each side by '24'.
-0.04166666667 + -0.1666666667a2 + a4 = 0

Move the constant term to the right:

Add '0.04166666667' to each side of the equation.
-0.04166666667 + -0.1666666667a2 + 0.04166666667 + a4 = 0 + 0.04166666667

Reorder the terms:
-0.04166666667 + 0.04166666667 + -0.1666666667a2 + a4 = 0 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + -0.1666666667a2 + a4 = 0 + 0.04166666667
-0.1666666667a2 + a4 = 0 + 0.04166666667

Combine like terms: 0 + 0.04166666667 = 0.04166666667
-0.1666666667a2 + a4 = 0.04166666667

The a term is -0.1666666667a2.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667a2 + 0.006944444447 + a4 = 0.04166666667 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667a2 + a4 = 0.04166666667 + 0.006944444447

Combine like terms: 0.04166666667 + 0.006944444447 = 0.048611111117
0.006944444447 + -0.1666666667a2 + a4 = 0.048611111117

Factor a perfect square on the left side:
(a2 + -0.08333333335)(a2 + -0.08333333335) = 0.048611111117

Calculate the square root of the right side: 0.220479276

Break this problem into two subproblems by setting 
(a2 + -0.08333333335) equal to 0.220479276 and -0.220479276.

Subproblem 1

a2 + -0.08333333335 = 0.220479276 Simplifying a2 + -0.08333333335 = 0.220479276 Reorder the terms: -0.08333333335 + a2 = 0.220479276 Solving -0.08333333335 + a2 = 0.220479276 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + a2 = 0.220479276 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + a2 = 0.220479276 + 0.08333333335 a2 = 0.220479276 + 0.08333333335 Combine like terms: 0.220479276 + 0.08333333335 = 0.30381260935 a2 = 0.30381260935 Simplifying a2 = 0.30381260935 Take the square root of each side: a = {-0.55119199, 0.55119199}

Subproblem 2

a2 + -0.08333333335 = -0.220479276 Simplifying a2 + -0.08333333335 = -0.220479276 Reorder the terms: -0.08333333335 + a2 = -0.220479276 Solving -0.08333333335 + a2 = -0.220479276 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + a2 = -0.220479276 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + a2 = -0.220479276 + 0.08333333335 a2 = -0.220479276 + 0.08333333335 Combine like terms: -0.220479276 + 0.08333333335 = -0.13714594265 a2 = -0.13714594265 Simplifying a2 = -0.13714594265 Reorder the terms: 0.13714594265 + a2 = -0.13714594265 + 0.13714594265 Combine like terms: -0.13714594265 + 0.13714594265 = 0.00000000000 0.13714594265 + a2 = 0.00000000000 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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