X^2-9X-52.75=0

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Solution for X^2-9X-52.75=0 equation: 


Simplifying
X2 + -9X + -52.75 = 0

Reorder the terms:
-52.75 + -9X + X2 = 0

Solving
-52.75 + -9X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '52.75' to each side of the equation.
-52.75 + -9X + 52.75 + X2 = 0 + 52.75

Reorder the terms:
-52.75 + 52.75 + -9X + X2 = 0 + 52.75

Combine like terms: -52.75 + 52.75 = 0.00
0.00 + -9X + X2 = 0 + 52.75
-9X + X2 = 0 + 52.75

Combine like terms: 0 + 52.75 = 52.75
-9X + X2 = 52.75

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 = 52.75 + 20.25

Reorder the terms:
20.25 + -9X + X2 = 52.75 + 20.25

Combine like terms: 52.75 + 20.25 = 73
20.25 + -9X + X2 = 73

Factor a perfect square on the left side:
(X + -4.5)(X + -4.5) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(X + -4.5) equal to 8.544003745 and -8.544003745.


Subproblem 1
X + -4.5 = 8.544003745

Simplifying
X + -4.5 = 8.544003745

Reorder the terms:
-4.5 + X = 8.544003745

Solving
-4.5 + X = 8.544003745

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 = 8.544003745 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + X = 8.544003745 + 4.5
X = 8.544003745 + 4.5

Combine like terms: 8.544003745 + 4.5 = 13.044003745
X = 13.044003745

Simplifying
X = 13.044003745


Subproblem 2
X + -4.5 = -8.544003745

Simplifying
X + -4.5 = -8.544003745

Reorder the terms:
-4.5 + X = -8.544003745

Solving
-4.5 + X = -8.544003745

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 = -8.544003745 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + X = -8.544003745 + 4.5
X = -8.544003745 + 4.5

Combine like terms: -8.544003745 + 4.5 = -4.044003745
X = -4.044003745

Simplifying
X = -4.044003745


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {13.044003745, -4.044003745}

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