(4x^2+1)(4x^2-1)=

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Solution for (4x^2+1)(4x^2-1)= equation:


Simplifying
(4x2 + 1)(4x2 + -1) = 0

Reorder the terms:
(1 + 4x2)(4x2 + -1) = 0

Reorder the terms:
(1 + 4x2)(-1 + 4x2) = 0

Multiply (1 + 4x2) * (-1 + 4x2)
(1(-1 + 4x2) + 4x2 * (-1 + 4x2)) = 0
((-1 * 1 + 4x2 * 1) + 4x2 * (-1 + 4x2)) = 0
((-1 + 4x2) + 4x2 * (-1 + 4x2)) = 0
(-1 + 4x2 + (-1 * 4x2 + 4x2 * 4x2)) = 0
(-1 + 4x2 + (-4x2 + 16x4)) = 0

Combine like terms: 4x2 + -4x2 = 0
(-1 + 0 + 16x4) = 0
(-1 + 16x4) = 0

Solving
-1 + 16x4 = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + 16x4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 16x4 = 0 + 1
16x4 = 0 + 1

Combine like terms: 0 + 1 = 1
16x4 = 1

Divide each side by '16'.
x4 = 0.0625

Simplifying
x4 = 0.0625

Reorder the terms:
-0.0625 + x4 = 0.0625 + -0.0625

Combine like terms: 0.0625 + -0.0625 = 0.0000
-0.0625 + x4 = 0.0000

Factor a difference between two squares.
(0.25 + x2)(-0.25 + x2) = 0.0000

Factor a difference between two squares.
(0.25 + x2)((0.5 + x)(-0.5 + x)) = 0.0000

Subproblem 1

Set the factor '(0.25 + x2)' equal to zero and attempt to solve: Simplifying 0.25 + x2 = 0 Solving 0.25 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x2 = 0 + -0.25 x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 x2 = -0.25 Simplifying x2 = -0.25 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(0.5 + x)' equal to zero and attempt to solve: Simplifying 0.5 + x = 0 Solving 0.5 + x = 0 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 + x = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0 + -0.5 x = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 x = -0.5 Simplifying x = -0.5

Subproblem 3

Set the factor '(-0.5 + x)' equal to zero and attempt to solve: Simplifying -0.5 + x = 0 Solving -0.5 + x = 0 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 + x = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0 + 0.5 x = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 x = 0.5 Simplifying x = 0.5

Solution

x = {-0.5, 0.5}

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