x^2+48x+576=11

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Solution for x^2+48x+576=11 equation: 


Simplifying
x2 + 48x + 576 = 11

Reorder the terms:
576 + 48x + x2 = 11

Solving
576 + 48x + x2 = 11

Solving for variable 'x'.

Reorder the terms:
576 + -11 + 48x + x2 = 11 + -11

Combine like terms: 576 + -11 = 565
565 + 48x + x2 = 11 + -11

Combine like terms: 11 + -11 = 0
565 + 48x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-565' to each side of the equation.
565 + 48x + -565 + x2 = 0 + -565

Reorder the terms:
565 + -565 + 48x + x2 = 0 + -565

Combine like terms: 565 + -565 = 0
0 + 48x + x2 = 0 + -565
48x + x2 = 0 + -565

Combine like terms: 0 + -565 = -565
48x + x2 = -565

The x term is 48x.  Take half its coefficient (24).
Square it (576) and add it to both sides.

Add '576' to each side of the equation.
48x + 576 + x2 = -565 + 576

Reorder the terms:
576 + 48x + x2 = -565 + 576

Combine like terms: -565 + 576 = 11
576 + 48x + x2 = 11

Factor a perfect square on the left side:
(x + 24)(x + 24) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + 24) equal to 3.31662479 and -3.31662479.


Subproblem 1
x + 24 = 3.31662479

Simplifying
x + 24 = 3.31662479

Reorder the terms:
24 + x = 3.31662479

Solving
24 + x = 3.31662479

Solving for variable 'x'.

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

Add '-24' to each side of the equation.
24 + -24 + x = 3.31662479 + -24

Combine like terms: 24 + -24 = 0
0 + x = 3.31662479 + -24
x = 3.31662479 + -24

Combine like terms: 3.31662479 + -24 = -20.68337521
x = -20.68337521

Simplifying
x = -20.68337521


Subproblem 2
x + 24 = -3.31662479

Simplifying
x + 24 = -3.31662479

Reorder the terms:
24 + x = -3.31662479

Solving
24 + x = -3.31662479

Solving for variable 'x'.

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

Add '-24' to each side of the equation.
24 + -24 + x = -3.31662479 + -24

Combine like terms: 24 + -24 = 0
0 + x = -3.31662479 + -24
x = -3.31662479 + -24

Combine like terms: -3.31662479 + -24 = -27.31662479
x = -27.31662479

Simplifying
x = -27.31662479


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-20.68337521, -27.31662479}

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