x^4-9x^2-16=0

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Solution for x^4-9x^2-16=0 equation:


Simplifying
x4 + -9x2 + -16 = 0

Reorder the terms:
-16 + -9x2 + x4 = 0

Solving
-16 + -9x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -9x2 + 16 + x4 = 0 + 16

Reorder the terms:
-16 + 16 + -9x2 + x4 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -9x2 + x4 = 0 + 16
-9x2 + x4 = 0 + 16

Combine like terms: 0 + 16 = 16
-9x2 + x4 = 16

The x term is -9x2.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x2 + 20.25 + x4 = 16 + 20.25

Reorder the terms:
20.25 + -9x2 + x4 = 16 + 20.25

Combine like terms: 16 + 20.25 = 36.25
20.25 + -9x2 + x4 = 36.25

Factor a perfect square on the left side:
(x2 + -4.5)(x2 + -4.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(x2 + -4.5) equal to 6.020797289 and -6.020797289.

Subproblem 1

x2 + -4.5 = 6.020797289 Simplifying x2 + -4.5 = 6.020797289 Reorder the terms: -4.5 + x2 = 6.020797289 Solving -4.5 + x2 = 6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x2 = 6.020797289 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = 6.020797289 + 4.5 x2 = 6.020797289 + 4.5 Combine like terms: 6.020797289 + 4.5 = 10.520797289 x2 = 10.520797289 Simplifying x2 = 10.520797289 Take the square root of each side: x = {-3.243577853, 3.243577853}

Subproblem 2

x2 + -4.5 = -6.020797289 Simplifying x2 + -4.5 = -6.020797289 Reorder the terms: -4.5 + x2 = -6.020797289 Solving -4.5 + x2 = -6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x2 = -6.020797289 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = -6.020797289 + 4.5 x2 = -6.020797289 + 4.5 Combine like terms: -6.020797289 + 4.5 = -1.520797289 x2 = -1.520797289 Simplifying x2 = -1.520797289 Reorder the terms: 1.520797289 + x2 = -1.520797289 + 1.520797289 Combine like terms: -1.520797289 + 1.520797289 = 0.000000000 1.520797289 + 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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