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 = 19.515301344
x = 19.515301344

Simplifying
x = 19.515301344


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 = -29.515301344
x = -29.515301344

Simplifying
x = -29.515301344


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

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