X^2-30-9X=0

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Solution for X^2-30-9X=0 equation: 


Simplifying
X2 + -30 + -9X = 0

Reorder the terms:
-30 + -9X + X2 = 0

Solving
-30 + -9X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -9X + 30 + X2 = 0 + 30

Reorder the terms:
-30 + 30 + -9X + X2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -9X + X2 = 0 + 30
-9X + X2 = 0 + 30

Combine like terms: 0 + 30 = 30
-9X + X2 = 30

The X term is -9X.  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.
-9X + 20.25 + X2 = 30 + 20.25

Reorder the terms:
20.25 + -9X + X2 = 30 + 20.25

Combine like terms: 30 + 20.25 = 50.25
20.25 + -9X + X2 = 50.25

Factor a perfect square on the left side:
(X + -4.5)(X + -4.5) = 50.25

Calculate the square root of the right side: 7.088723439

Break this problem into two subproblems by setting 
(X + -4.5) equal to 7.088723439 and -7.088723439.


Subproblem 1
X + -4.5 = 7.088723439

Simplifying
X + -4.5 = 7.088723439

Reorder the terms:
-4.5 + X = 7.088723439

Solving
-4.5 + X = 7.088723439

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 + X = 7.088723439 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + X = 7.088723439 + 4.5
X = 7.088723439 + 4.5

Combine like terms: 7.088723439 + 4.5 = 11.588723439
X = 11.588723439

Simplifying
X = 11.588723439


Subproblem 2
X + -4.5 = -7.088723439

Simplifying
X + -4.5 = -7.088723439

Reorder the terms:
-4.5 + X = -7.088723439

Solving
-4.5 + X = -7.088723439

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 + X = -7.088723439 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + X = -7.088723439 + 4.5
X = -7.088723439 + 4.5

Combine like terms: -7.088723439 + 4.5 = -2.588723439
X = -2.588723439

Simplifying
X = -2.588723439


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {11.588723439, -2.588723439}

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