16x^4-16x^2-3=0

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Solution for 16x^4-16x^2-3=0 equation:


Simplifying
16x4 + -16x2 + -3 = 0

Reorder the terms:
-3 + -16x2 + 16x4 = 0

Solving
-3 + -16x2 + 16x4 = 0

Solving for variable 'x'.

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

Divide each side by '16'.
-0.1875 + -1x2 + x4 = 0

Move the constant term to the right:

Add '0.1875' to each side of the equation.
-0.1875 + -1x2 + 0.1875 + x4 = 0 + 0.1875

Reorder the terms:
-0.1875 + 0.1875 + -1x2 + x4 = 0 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + -1x2 + x4 = 0 + 0.1875
-1x2 + x4 = 0 + 0.1875

Combine like terms: 0 + 0.1875 = 0.1875
-1x2 + x4 = 0.1875

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 = 0.1875 + 0.25

Reorder the terms:
0.25 + -1x2 + x4 = 0.1875 + 0.25

Combine like terms: 0.1875 + 0.25 = 0.4375
0.25 + -1x2 + x4 = 0.4375

Factor a perfect square on the left side:
(x2 + -0.5)(x2 + -0.5) = 0.4375

Calculate the square root of the right side: 0.661437828

Break this problem into two subproblems by setting 
(x2 + -0.5) equal to 0.661437828 and -0.661437828.

Subproblem 1

x2 + -0.5 = 0.661437828 Simplifying x2 + -0.5 = 0.661437828 Reorder the terms: -0.5 + x2 = 0.661437828 Solving -0.5 + x2 = 0.661437828 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 = 0.661437828 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = 0.661437828 + 0.5 x2 = 0.661437828 + 0.5 Combine like terms: 0.661437828 + 0.5 = 1.161437828 x2 = 1.161437828 Simplifying x2 = 1.161437828 Take the square root of each side: x = {-1.07770025, 1.07770025}

Subproblem 2

x2 + -0.5 = -0.661437828 Simplifying x2 + -0.5 = -0.661437828 Reorder the terms: -0.5 + x2 = -0.661437828 Solving -0.5 + x2 = -0.661437828 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 = -0.661437828 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = -0.661437828 + 0.5 x2 = -0.661437828 + 0.5 Combine like terms: -0.661437828 + 0.5 = -0.161437828 x2 = -0.161437828 Simplifying x2 = -0.161437828 Reorder the terms: 0.161437828 + x2 = -0.161437828 + 0.161437828 Combine like terms: -0.161437828 + 0.161437828 = 0.000000000 0.161437828 + 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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