9x^6-63x^5+63x^4=

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Solution for 9x^6-63x^5+63x^4= equation: 


Simplifying
9x6 + -63x5 + 63x4 = 0

Reorder the terms:
63x4 + -63x5 + 9x6 = 0

Solving
63x4 + -63x5 + 9x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9x4'.
9x4(7 + -7x + x2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve:

Simplifying
x4 = 0

Solving
x4 = 0

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

Simplifying
x4 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(7 + -7x + x2)' equal to zero and attempt to solve:

Simplifying
7 + -7x + x2 = 0

Solving
7 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -7x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + -7x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -7x + x2 = 0 + -7
-7x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-7x + x2 = -7

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -7 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -7 + 12.25

Combine like terms: -7 + 12.25 = 5.25
12.25 + -7x + x2 = 5.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + -3.5) equal to 2.291287847 and -2.291287847.


Subproblem 1
x + -3.5 = 2.291287847

Simplifying
x + -3.5 = 2.291287847

Reorder the terms:
-3.5 + x = 2.291287847

Solving
-3.5 + x = 2.291287847

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 2.291287847 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 2.291287847 + 3.5
x = 2.291287847 + 3.5

Combine like terms: 2.291287847 + 3.5 = 5.791287847
x = 5.791287847

Simplifying
x = 5.791287847


Subproblem 2
x + -3.5 = -2.291287847

Simplifying
x + -3.5 = -2.291287847

Reorder the terms:
-3.5 + x = -2.291287847

Solving
-3.5 + x = -2.291287847

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -2.291287847 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -2.291287847 + 3.5
x = -2.291287847 + 3.5

Combine like terms: -2.291287847 + 3.5 = 1.208712153
x = 1.208712153

Simplifying
x = 1.208712153


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.791287847, 1.208712153}
Solution
x = {5.791287847, 1.208712153}

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