9x^7-45x^6+18x^5=

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Solution for 9x^7-45x^6+18x^5= equation: 


Simplifying
9x7 + -45x6 + 18x5 = 0

Reorder the terms:
18x5 + -45x6 + 9x7 = 0

Solving
18x5 + -45x6 + 9x7 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9x5'.
9x5(2 + -5x + x2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor 'x5' equal to zero and attempt to solve:

Simplifying
x5 = 0

Solving
x5 = 0

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

Simplifying
x5 = 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 '(2 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
2 + -5x + x2 = 0

Solving
2 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -5x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -5x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x + x2 = 0 + -2
-5x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-5x + x2 = -2

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 = -2 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -2 + 6.25

Combine like terms: -2 + 6.25 = 4.25
6.25 + -5x + x2 = 4.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
x + -2.5 = 2.061552813

Simplifying
x + -2.5 = 2.061552813

Reorder the terms:
-2.5 + x = 2.061552813

Solving
-2.5 + x = 2.061552813

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 2.061552813 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.061552813 + 2.5
x = 2.061552813 + 2.5

Combine like terms: 2.061552813 + 2.5 = 4.561552813
x = 4.561552813

Simplifying
x = 4.561552813


Subproblem 2
x + -2.5 = -2.061552813

Simplifying
x + -2.5 = -2.061552813

Reorder the terms:
-2.5 + x = -2.061552813

Solving
-2.5 + x = -2.061552813

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -2.061552813 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.061552813 + 2.5
x = -2.061552813 + 2.5

Combine like terms: -2.061552813 + 2.5 = 0.438447187
x = 0.438447187

Simplifying
x = 0.438447187


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.561552813, 0.438447187}
Solution
x = {4.561552813, 0.438447187}

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