x^4-x^2-45=0

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Solution for x^4-x^2-45=0 equation:


Simplifying
x4 + -1x2 + -45 = 0

Reorder the terms:
-45 + -1x2 + x4 = 0

Solving
-45 + -1x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + -1x2 + 45 + x4 = 0 + 45

Reorder the terms:
-45 + 45 + -1x2 + x4 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + -1x2 + x4 = 0 + 45
-1x2 + x4 = 0 + 45

Combine like terms: 0 + 45 = 45
-1x2 + x4 = 45

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 = 45 + 0.25

Reorder the terms:
0.25 + -1x2 + x4 = 45 + 0.25

Combine like terms: 45 + 0.25 = 45.25
0.25 + -1x2 + x4 = 45.25

Factor a perfect square on the left side:
(x2 + -0.5)(x2 + -0.5) = 45.25

Calculate the square root of the right side: 6.726812024

Break this problem into two subproblems by setting 
(x2 + -0.5) equal to 6.726812024 and -6.726812024.

Subproblem 1

x2 + -0.5 = 6.726812024 Simplifying x2 + -0.5 = 6.726812024 Reorder the terms: -0.5 + x2 = 6.726812024 Solving -0.5 + x2 = 6.726812024 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 = 6.726812024 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = 6.726812024 + 0.5 x2 = 6.726812024 + 0.5 Combine like terms: 6.726812024 + 0.5 = 7.226812024 x2 = 7.226812024 Simplifying x2 = 7.226812024 Take the square root of each side: x = {-2.688273056, 2.688273056}

Subproblem 2

x2 + -0.5 = -6.726812024 Simplifying x2 + -0.5 = -6.726812024 Reorder the terms: -0.5 + x2 = -6.726812024 Solving -0.5 + x2 = -6.726812024 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 = -6.726812024 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = -6.726812024 + 0.5 x2 = -6.726812024 + 0.5 Combine like terms: -6.726812024 + 0.5 = -6.226812024 x2 = -6.226812024 Simplifying x2 = -6.226812024 Reorder the terms: 6.226812024 + x2 = -6.226812024 + 6.226812024 Combine like terms: -6.226812024 + 6.226812024 = 0.000000000 6.226812024 + 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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