x^4+x^2-1.5=0

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Solution for x^4+x^2-1.5=0 equation:


Simplifying
x4 + x2 + -1.5 = 0

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

Solving
-1.5 + x2 + 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 + x2 + 1.5 + x4 = 0 + 1.5

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

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

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

The x term is x2.  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.
x2 + 0.25 + x4 = 1.5 + 0.25

Reorder the terms:
0.25 + x2 + x4 = 1.5 + 0.25

Combine like terms: 1.5 + 0.25 = 1.75
0.25 + x2 + x4 = 1.75

Factor a perfect square on the left side:
(x2 + 0.5)(x2 + 0.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(x2 + 0.5) equal to 1.322875656 and -1.322875656.

Subproblem 1

x2 + 0.5 = 1.322875656 Simplifying x2 + 0.5 = 1.322875656 Reorder the terms: 0.5 + x2 = 1.322875656 Solving 0.5 + x2 = 1.322875656 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 = 1.322875656 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 1.322875656 + -0.5 x2 = 1.322875656 + -0.5 Combine like terms: 1.322875656 + -0.5 = 0.822875656 x2 = 0.822875656 Simplifying x2 = 0.822875656 Take the square root of each side: x = {-0.90712494, 0.90712494}

Subproblem 2

x2 + 0.5 = -1.322875656 Simplifying x2 + 0.5 = -1.322875656 Reorder the terms: 0.5 + x2 = -1.322875656 Solving 0.5 + x2 = -1.322875656 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 = -1.322875656 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -1.322875656 + -0.5 x2 = -1.322875656 + -0.5 Combine like terms: -1.322875656 + -0.5 = -1.822875656 x2 = -1.822875656 Simplifying x2 = -1.822875656 Reorder the terms: 1.822875656 + x2 = -1.822875656 + 1.822875656 Combine like terms: -1.822875656 + 1.822875656 = 0.000000000 1.822875656 + 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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