x^2-20x+32=0

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Solution for x^2-20x+32=0 equation: 


Simplifying
x2 + -20x + 32 = 0

Reorder the terms:
32 + -20x + x2 = 0

Solving
32 + -20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + -20x + -32 + x2 = 0 + -32

Reorder the terms:
32 + -32 + -20x + x2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -20x + x2 = 0 + -32
-20x + x2 = 0 + -32

Combine like terms: 0 + -32 = -32
-20x + x2 = -32

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 = -32 + 100

Reorder the terms:
100 + -20x + x2 = -32 + 100

Combine like terms: -32 + 100 = 68
100 + -20x + x2 = 68

Factor a perfect square on the left side:
(x + -10)(x + -10) = 68

Calculate the square root of the right side: 8.246211251

Break this problem into two subproblems by setting 
(x + -10) equal to 8.246211251 and -8.246211251.


Subproblem 1
x + -10 = 8.246211251

Simplifying
x + -10 = 8.246211251

Reorder the terms:
-10 + x = 8.246211251

Solving
-10 + x = 8.246211251

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 = 8.246211251 + 10

Combine like terms: -10 + 10 = 0
0 + x = 8.246211251 + 10
x = 8.246211251 + 10

Combine like terms: 8.246211251 + 10 = 18.246211251
x = 18.246211251

Simplifying
x = 18.246211251


Subproblem 2
x + -10 = -8.246211251

Simplifying
x + -10 = -8.246211251

Reorder the terms:
-10 + x = -8.246211251

Solving
-10 + x = -8.246211251

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 = -8.246211251 + 10

Combine like terms: -10 + 10 = 0
0 + x = -8.246211251 + 10
x = -8.246211251 + 10

Combine like terms: -8.246211251 + 10 = 1.753788749
x = 1.753788749

Simplifying
x = 1.753788749


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.246211251, 1.753788749}

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