x^2-21x+36=0

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Solution for x^2-21x+36=0 equation: 


Simplifying
x2 + -21x + 36 = 0

Reorder the terms:
36 + -21x + x2 = 0

Solving
36 + -21x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + -21x + -36 + x2 = 0 + -36

Reorder the terms:
36 + -36 + -21x + x2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -21x + x2 = 0 + -36
-21x + x2 = 0 + -36

Combine like terms: 0 + -36 = -36
-21x + x2 = -36

The x term is -21x.  Take half its coefficient (-10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
-21x + 110.25 + x2 = -36 + 110.25

Reorder the terms:
110.25 + -21x + x2 = -36 + 110.25

Combine like terms: -36 + 110.25 = 74.25
110.25 + -21x + x2 = 74.25

Factor a perfect square on the left side:
(x + -10.5)(x + -10.5) = 74.25

Calculate the square root of the right side: 8.61684397

Break this problem into two subproblems by setting 
(x + -10.5) equal to 8.61684397 and -8.61684397.


Subproblem 1
x + -10.5 = 8.61684397

Simplifying
x + -10.5 = 8.61684397

Reorder the terms:
-10.5 + x = 8.61684397

Solving
-10.5 + x = 8.61684397

Solving for variable 'x'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + x = 8.61684397 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = 8.61684397 + 10.5
x = 8.61684397 + 10.5

Combine like terms: 8.61684397 + 10.5 = 19.11684397
x = 19.11684397

Simplifying
x = 19.11684397


Subproblem 2
x + -10.5 = -8.61684397

Simplifying
x + -10.5 = -8.61684397

Reorder the terms:
-10.5 + x = -8.61684397

Solving
-10.5 + x = -8.61684397

Solving for variable 'x'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + x = -8.61684397 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = -8.61684397 + 10.5
x = -8.61684397 + 10.5

Combine like terms: -8.61684397 + 10.5 = 1.88315603
x = 1.88315603

Simplifying
x = 1.88315603


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.11684397, 1.88315603}

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