x^2-20x-3276=0

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Solution for x^2-20x-3276=0 equation: 


Simplifying
x2 + -20x + -3276 = 0

Reorder the terms:
-3276 + -20x + x2 = 0

Solving
-3276 + -20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '3276' to each side of the equation.
-3276 + -20x + 3276 + x2 = 0 + 3276

Reorder the terms:
-3276 + 3276 + -20x + x2 = 0 + 3276

Combine like terms: -3276 + 3276 = 0
0 + -20x + x2 = 0 + 3276
-20x + x2 = 0 + 3276

Combine like terms: 0 + 3276 = 3276
-20x + x2 = 3276

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 = 3276 + 100

Reorder the terms:
100 + -20x + x2 = 3276 + 100

Combine like terms: 3276 + 100 = 3376
100 + -20x + x2 = 3376

Factor a perfect square on the left side:
(x + -10)(x + -10) = 3376

Calculate the square root of the right side: 58.103356185

Break this problem into two subproblems by setting 
(x + -10) equal to 58.103356185 and -58.103356185.


Subproblem 1
x + -10 = 58.103356185

Simplifying
x + -10 = 58.103356185

Reorder the terms:
-10 + x = 58.103356185

Solving
-10 + x = 58.103356185

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 = 58.103356185 + 10

Combine like terms: -10 + 10 = 0
0 + x = 58.103356185 + 10
x = 58.103356185 + 10

Combine like terms: 58.103356185 + 10 = 68.103356185
x = 68.103356185

Simplifying
x = 68.103356185


Subproblem 2
x + -10 = -58.103356185

Simplifying
x + -10 = -58.103356185

Reorder the terms:
-10 + x = -58.103356185

Solving
-10 + x = -58.103356185

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 = -58.103356185 + 10

Combine like terms: -10 + 10 = 0
0 + x = -58.103356185 + 10
x = -58.103356185 + 10

Combine like terms: -58.103356185 + 10 = -48.103356185
x = -48.103356185

Simplifying
x = -48.103356185


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {68.103356185, -48.103356185}

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