x^4=5x^3-9x^2

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Solution for x^4=5x^3-9x^2 equation: 


Simplifying
x4 = 5x3 + -9x2

Reorder the terms:
x4 = -9x2 + 5x3

Solving
x4 = -9x2 + 5x3

Solving for variable 'x'.

Reorder the terms:
9x2 + -5x3 + x4 = -9x2 + 5x3 + 9x2 + -5x3

Reorder the terms:
9x2 + -5x3 + x4 = -9x2 + 9x2 + 5x3 + -5x3

Combine like terms: -9x2 + 9x2 = 0
9x2 + -5x3 + x4 = 0 + 5x3 + -5x3
9x2 + -5x3 + x4 = 5x3 + -5x3

Combine like terms: 5x3 + -5x3 = 0
9x2 + -5x3 + x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(9 + -5x + x2) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(9 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
9 + -5x + x2 = 0

Solving
9 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -5x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + -5x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5x + x2 = 0 + -9
-5x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
-5x + x2 = -9

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -9 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -9 + 6.25

Combine like terms: -9 + 6.25 = -2.75
6.25 + -5x + x2 = -2.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = -2.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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