x^2-10x+16.5=0

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Solution for x^2-10x+16.5=0 equation: 


Simplifying
x2 + -10x + 16.5 = 0

Reorder the terms:
16.5 + -10x + x2 = 0

Solving
16.5 + -10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-16.5' to each side of the equation.
16.5 + -10x + -16.5 + x2 = 0 + -16.5

Reorder the terms:
16.5 + -16.5 + -10x + x2 = 0 + -16.5

Combine like terms: 16.5 + -16.5 = 0.0
0.0 + -10x + x2 = 0 + -16.5
-10x + x2 = 0 + -16.5

Combine like terms: 0 + -16.5 = -16.5
-10x + x2 = -16.5

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -16.5 + 25

Reorder the terms:
25 + -10x + x2 = -16.5 + 25

Combine like terms: -16.5 + 25 = 8.5
25 + -10x + x2 = 8.5

Factor a perfect square on the left side:
(x + -5)(x + -5) = 8.5

Calculate the square root of the right side: 2.915475947

Break this problem into two subproblems by setting 
(x + -5) equal to 2.915475947 and -2.915475947.


Subproblem 1
x + -5 = 2.915475947

Simplifying
x + -5 = 2.915475947

Reorder the terms:
-5 + x = 2.915475947

Solving
-5 + x = 2.915475947

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 2.915475947 + 5

Combine like terms: -5 + 5 = 0
0 + x = 2.915475947 + 5
x = 2.915475947 + 5

Combine like terms: 2.915475947 + 5 = 7.915475947
x = 7.915475947

Simplifying
x = 7.915475947


Subproblem 2
x + -5 = -2.915475947

Simplifying
x + -5 = -2.915475947

Reorder the terms:
-5 + x = -2.915475947

Solving
-5 + x = -2.915475947

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -2.915475947 + 5

Combine like terms: -5 + 5 = 0
0 + x = -2.915475947 + 5
x = -2.915475947 + 5

Combine like terms: -2.915475947 + 5 = 2.084524053
x = 2.084524053

Simplifying
x = 2.084524053


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.915475947, 2.084524053}

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