x^2-20x+11=

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Solution for x^2-20x+11= equation: 


Simplifying
x2 + -20x + 11 = 0

Reorder the terms:
11 + -20x + x2 = 0

Solving
11 + -20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -20x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + -20x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -20x + x2 = 0 + -11
-20x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
-20x + x2 = -11

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -11 + 100

Reorder the terms:
100 + -20x + x2 = -11 + 100

Combine like terms: -11 + 100 = 89
100 + -20x + x2 = 89

Factor a perfect square on the left side:
(x + -10)(x + -10) = 89

Calculate the square root of the right side: 9.433981132

Break this problem into two subproblems by setting 
(x + -10) equal to 9.433981132 and -9.433981132.


Subproblem 1
x + -10 = 9.433981132

Simplifying
x + -10 = 9.433981132

Reorder the terms:
-10 + x = 9.433981132

Solving
-10 + x = 9.433981132

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = 9.433981132 + 10

Combine like terms: -10 + 10 = 0
0 + x = 9.433981132 + 10
x = 9.433981132 + 10

Combine like terms: 9.433981132 + 10 = 19.433981132
x = 19.433981132

Simplifying
x = 19.433981132


Subproblem 2
x + -10 = -9.433981132

Simplifying
x + -10 = -9.433981132

Reorder the terms:
-10 + x = -9.433981132

Solving
-10 + x = -9.433981132

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = -9.433981132 + 10

Combine like terms: -10 + 10 = 0
0 + x = -9.433981132 + 10
x = -9.433981132 + 10

Combine like terms: -9.433981132 + 10 = 0.566018868
x = 0.566018868

Simplifying
x = 0.566018868


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.433981132, 0.566018868}

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