(x^2+1)(x^2-1.5)=0

Solution for (x^2+1)(x^2-1.5)=0 equation:

Simplifying
(x2 + 1)(x2 + -1.5) = 0

Reorder the terms:
(1 + x2)(x2 + -1.5) = 0

Reorder the terms:
(1 + x2)(-1.5 + x2) = 0

Multiply (1 + x2) * (-1.5 + x2)
(1(-1.5 + x2) + x2(-1.5 + x2)) = 0
((-1.5 * 1 + x2 * 1) + x2(-1.5 + x2)) = 0
((-1.5 + 1x2) + x2(-1.5 + x2)) = 0
(-1.5 + 1x2 + (-1.5 * x2 + x2 * x2)) = 0
(-1.5 + 1x2 + (-1.5x2 + x4)) = 0

Combine like terms: 1x2 + -1.5x2 = -0.5x2
(-1.5 + -0.5x2 + x4) = 0

Solving
-1.5 + -0.5x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -0.5x2 + 1.5 + x4 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -0.5x2 + x4 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -0.5x2 + x4 = 0 + 1.5
-0.5x2 + x4 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-0.5x2 + x4 = 1.5

The x term is -0.5x2.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x2 + 0.0625 + x4 = 1.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x2 + x4 = 1.5 + 0.0625

Combine like terms: 1.5 + 0.0625 = 1.5625
0.0625 + -0.5x2 + x4 = 1.5625

Factor a perfect square on the left side:
(x2 + -0.25)(x2 + -0.25) = 1.5625

Calculate the square root of the right side: 1.25

Break this problem into two subproblems by setting 
(x2 + -0.25) equal to 1.25 and -1.25.

Subproblem 1
x2 + -0.25 = 1.25

Simplifying
x2 + -0.25 = 1.25

Reorder the terms:
-0.25 + x2 = 1.25

Solving
-0.25 + x2 = 1.25

Solving for variable 'x'.

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 = 1.25 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x2 = 1.25 + 0.25
x2 = 1.25 + 0.25

Combine like terms: 1.25 + 0.25 = 1.5
x2 = 1.5

Simplifying
x2 = 1.5

Take the square root of each side:
x = {-1.224744871, 1.224744871}

Subproblem 2
x2 + -0.25 = -1.25

Simplifying
x2 + -0.25 = -1.25

Reorder the terms:
-0.25 + x2 = -1.25

Solving
-0.25 + x2 = -1.25

Solving for variable 'x'.

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 = -1.25 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x2 = -1.25 + 0.25
x2 = -1.25 + 0.25

Combine like terms: -1.25 + 0.25 = -1
x2 = -1

Simplifying
x2 = -1

Reorder the terms:
1 + x2 = -1 + 1

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

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.