x^2-10x-576=0

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Solution for x^2-10x-576=0 equation: 


Simplifying
x2 + -10x + -576 = 0

Reorder the terms:
-576 + -10x + x2 = 0

Solving
-576 + -10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '576' to each side of the equation.
-576 + -10x + 576 + x2 = 0 + 576

Reorder the terms:
-576 + 576 + -10x + x2 = 0 + 576

Combine like terms: -576 + 576 = 0
0 + -10x + x2 = 0 + 576
-10x + x2 = 0 + 576

Combine like terms: 0 + 576 = 576
-10x + x2 = 576

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 576 + 25

Reorder the terms:
25 + -10x + x2 = 576 + 25

Combine like terms: 576 + 25 = 601
25 + -10x + x2 = 601

Factor a perfect square on the left side:
(x + -5)(x + -5) = 601

Calculate the square root of the right side: 24.515301344

Break this problem into two subproblems by setting 
(x + -5) equal to 24.515301344 and -24.515301344.


Subproblem 1
x + -5 = 24.515301344

Simplifying
x + -5 = 24.515301344

Reorder the terms:
-5 + x = 24.515301344

Solving
-5 + x = 24.515301344

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 24.515301344 + 5

Combine like terms: -5 + 5 = 0
0 + x = 24.515301344 + 5
x = 24.515301344 + 5

Combine like terms: 24.515301344 + 5 = 29.515301344
x = 29.515301344

Simplifying
x = 29.515301344


Subproblem 2
x + -5 = -24.515301344

Simplifying
x + -5 = -24.515301344

Reorder the terms:
-5 + x = -24.515301344

Solving
-5 + x = -24.515301344

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -24.515301344 + 5

Combine like terms: -5 + 5 = 0
0 + x = -24.515301344 + 5
x = -24.515301344 + 5

Combine like terms: -24.515301344 + 5 = -19.515301344
x = -19.515301344

Simplifying
x = -19.515301344


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {29.515301344, -19.515301344}

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