x^2+16x+53=0

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Solution for x^2+16x+53=0 equation: 


Simplifying
x2 + 16x + 53 = 0

Reorder the terms:
53 + 16x + x2 = 0

Solving
53 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-53' to each side of the equation.
53 + 16x + -53 + x2 = 0 + -53

Reorder the terms:
53 + -53 + 16x + x2 = 0 + -53

Combine like terms: 53 + -53 = 0
0 + 16x + x2 = 0 + -53
16x + x2 = 0 + -53

Combine like terms: 0 + -53 = -53
16x + x2 = -53

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = -53 + 64

Reorder the terms:
64 + 16x + x2 = -53 + 64

Combine like terms: -53 + 64 = 11
64 + 16x + x2 = 11

Factor a perfect square on the left side:
(x + 8)(x + 8) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + 8) equal to 3.31662479 and -3.31662479.


Subproblem 1
x + 8 = 3.31662479

Simplifying
x + 8 = 3.31662479

Reorder the terms:
8 + x = 3.31662479

Solving
8 + x = 3.31662479

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 3.31662479 + -8

Combine like terms: 8 + -8 = 0
0 + x = 3.31662479 + -8
x = 3.31662479 + -8

Combine like terms: 3.31662479 + -8 = -4.68337521
x = -4.68337521

Simplifying
x = -4.68337521


Subproblem 2
x + 8 = -3.31662479

Simplifying
x + 8 = -3.31662479

Reorder the terms:
8 + x = -3.31662479

Solving
8 + x = -3.31662479

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -3.31662479 + -8

Combine like terms: 8 + -8 = 0
0 + x = -3.31662479 + -8
x = -3.31662479 + -8

Combine like terms: -3.31662479 + -8 = -11.31662479
x = -11.31662479

Simplifying
x = -11.31662479


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-4.68337521, -11.31662479}

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