x^2-8.2x+10.05=0

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Solution for x^2-8.2x+10.05=0 equation: 


Simplifying
x2 + -8.2x + 10.05 = 0

Reorder the terms:
10.05 + -8.2x + x2 = 0

Solving
10.05 + -8.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-10.05' to each side of the equation.
10.05 + -8.2x + -10.05 + x2 = 0 + -10.05

Reorder the terms:
10.05 + -10.05 + -8.2x + x2 = 0 + -10.05

Combine like terms: 10.05 + -10.05 = 0.00
0.00 + -8.2x + x2 = 0 + -10.05
-8.2x + x2 = 0 + -10.05

Combine like terms: 0 + -10.05 = -10.05
-8.2x + x2 = -10.05

The x term is -8.2x.  Take half its coefficient (-4.1).
Square it (16.81) and add it to both sides.

Add '16.81' to each side of the equation.
-8.2x + 16.81 + x2 = -10.05 + 16.81

Reorder the terms:
16.81 + -8.2x + x2 = -10.05 + 16.81

Combine like terms: -10.05 + 16.81 = 6.76
16.81 + -8.2x + x2 = 6.76

Factor a perfect square on the left side:
(x + -4.1)(x + -4.1) = 6.76

Calculate the square root of the right side: 2.6

Break this problem into two subproblems by setting 
(x + -4.1) equal to 2.6 and -2.6.


Subproblem 1
x + -4.1 = 2.6

Simplifying
x + -4.1 = 2.6

Reorder the terms:
-4.1 + x = 2.6

Solving
-4.1 + x = 2.6

Solving for variable 'x'.

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

Add '4.1' to each side of the equation.
-4.1 + 4.1 + x = 2.6 + 4.1

Combine like terms: -4.1 + 4.1 = 0.0
0.0 + x = 2.6 + 4.1
x = 2.6 + 4.1

Combine like terms: 2.6 + 4.1 = 6.7
x = 6.7

Simplifying
x = 6.7


Subproblem 2
x + -4.1 = -2.6

Simplifying
x + -4.1 = -2.6

Reorder the terms:
-4.1 + x = -2.6

Solving
-4.1 + x = -2.6

Solving for variable 'x'.

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

Add '4.1' to each side of the equation.
-4.1 + 4.1 + x = -2.6 + 4.1

Combine like terms: -4.1 + 4.1 = 0.0
0.0 + x = -2.6 + 4.1
x = -2.6 + 4.1

Combine like terms: -2.6 + 4.1 = 1.5
x = 1.5

Simplifying
x = 1.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.7, 1.5}

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