X*X-45X-324=0

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Solution for X*X-45X-324=0 equation: 


Simplifying
X * X + -45X + -324 = 0

Multiply X * X
X2 + -45X + -324 = 0

Reorder the terms:
-324 + -45X + X2 = 0

Solving
-324 + -45X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '324' to each side of the equation.
-324 + -45X + 324 + X2 = 0 + 324

Reorder the terms:
-324 + 324 + -45X + X2 = 0 + 324

Combine like terms: -324 + 324 = 0
0 + -45X + X2 = 0 + 324
-45X + X2 = 0 + 324

Combine like terms: 0 + 324 = 324
-45X + X2 = 324

The X term is -45X.  Take half its coefficient (-22.5).
Square it (506.25) and add it to both sides.

Add '506.25' to each side of the equation.
-45X + 506.25 + X2 = 324 + 506.25

Reorder the terms:
506.25 + -45X + X2 = 324 + 506.25

Combine like terms: 324 + 506.25 = 830.25
506.25 + -45X + X2 = 830.25

Factor a perfect square on the left side:
(X + -22.5)(X + -22.5) = 830.25

Calculate the square root of the right side: 28.814059068

Break this problem into two subproblems by setting 
(X + -22.5) equal to 28.814059068 and -28.814059068.


Subproblem 1
X + -22.5 = 28.814059068

Simplifying
X + -22.5 = 28.814059068

Reorder the terms:
-22.5 + X = 28.814059068

Solving
-22.5 + X = 28.814059068

Solving for variable 'X'.

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

Add '22.5' to each side of the equation.
-22.5 + 22.5 + X = 28.814059068 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + X = 28.814059068 + 22.5
X = 28.814059068 + 22.5

Combine like terms: 28.814059068 + 22.5 = 51.314059068
X = 51.314059068

Simplifying
X = 51.314059068


Subproblem 2
X + -22.5 = -28.814059068

Simplifying
X + -22.5 = -28.814059068

Reorder the terms:
-22.5 + X = -28.814059068

Solving
-22.5 + X = -28.814059068

Solving for variable 'X'.

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

Add '22.5' to each side of the equation.
-22.5 + 22.5 + X = -28.814059068 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + X = -28.814059068 + 22.5
X = -28.814059068 + 22.5

Combine like terms: -28.814059068 + 22.5 = -6.314059068
X = -6.314059068

Simplifying
X = -6.314059068


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {51.314059068, -6.314059068}

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