x^2-20x-544=0

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Solution for x^2-20x-544=0 equation: 


Simplifying
x2 + -20x + -544 = 0

Reorder the terms:
-544 + -20x + x2 = 0

Solving
-544 + -20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '544' to each side of the equation.
-544 + -20x + 544 + x2 = 0 + 544

Reorder the terms:
-544 + 544 + -20x + x2 = 0 + 544

Combine like terms: -544 + 544 = 0
0 + -20x + x2 = 0 + 544
-20x + x2 = 0 + 544

Combine like terms: 0 + 544 = 544
-20x + x2 = 544

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 = 544 + 100

Reorder the terms:
100 + -20x + x2 = 544 + 100

Combine like terms: 544 + 100 = 644
100 + -20x + x2 = 644

Factor a perfect square on the left side:
(x + -10)(x + -10) = 644

Calculate the square root of the right side: 25.377155081

Break this problem into two subproblems by setting 
(x + -10) equal to 25.377155081 and -25.377155081.


Subproblem 1
x + -10 = 25.377155081

Simplifying
x + -10 = 25.377155081

Reorder the terms:
-10 + x = 25.377155081

Solving
-10 + x = 25.377155081

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 = 25.377155081 + 10

Combine like terms: -10 + 10 = 0
0 + x = 25.377155081 + 10
x = 25.377155081 + 10

Combine like terms: 25.377155081 + 10 = 35.377155081
x = 35.377155081

Simplifying
x = 35.377155081


Subproblem 2
x + -10 = -25.377155081

Simplifying
x + -10 = -25.377155081

Reorder the terms:
-10 + x = -25.377155081

Solving
-10 + x = -25.377155081

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 = -25.377155081 + 10

Combine like terms: -10 + 10 = 0
0 + x = -25.377155081 + 10
x = -25.377155081 + 10

Combine like terms: -25.377155081 + 10 = -15.377155081
x = -15.377155081

Simplifying
x = -15.377155081


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {35.377155081, -15.377155081}

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