x^2-11x+5.25=0

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Solution for x^2-11x+5.25=0 equation: 


Simplifying
x2 + -11x + 5.25 = 0

Reorder the terms:
5.25 + -11x + x2 = 0

Solving
5.25 + -11x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-5.25' to each side of the equation.
5.25 + -11x + -5.25 + x2 = 0 + -5.25

Reorder the terms:
5.25 + -5.25 + -11x + x2 = 0 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + -11x + x2 = 0 + -5.25
-11x + x2 = 0 + -5.25

Combine like terms: 0 + -5.25 = -5.25
-11x + x2 = -5.25

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = -5.25 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -5.25 + 30.25

Combine like terms: -5.25 + 30.25 = 25
30.25 + -11x + x2 = 25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 25

Calculate the square root of the right side: 5

Break this problem into two subproblems by setting 
(x + -5.5) equal to 5 and -5.


Subproblem 1
x + -5.5 = 5

Simplifying
x + -5.5 = 5

Reorder the terms:
-5.5 + x = 5

Solving
-5.5 + x = 5

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 5 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 5 + 5.5
x = 5 + 5.5

Combine like terms: 5 + 5.5 = 10.5
x = 10.5

Simplifying
x = 10.5


Subproblem 2
x + -5.5 = -5

Simplifying
x + -5.5 = -5

Reorder the terms:
-5.5 + x = -5

Solving
-5.5 + x = -5

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -5 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -5 + 5.5
x = -5 + 5.5

Combine like terms: -5 + 5.5 = 0.5
x = 0.5

Simplifying
x = 0.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.5, 0.5}

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