x(x)+16x+25=0

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Solution for x(x)+16x+25=0 equation:


Simplifying
x(x) + 16x + 25 = 0

Multiply x * x
x2 + 16x + 25 = 0

Reorder the terms:
25 + 16x + x2 = 0

Solving
25 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + 16x + -25 + x2 = 0 + -25

Reorder the terms:
25 + -25 + 16x + x2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 16x + x2 = 0 + -25
16x + x2 = 0 + -25

Combine like terms: 0 + -25 = -25
16x + x2 = -25

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 = -25 + 64

Reorder the terms:
64 + 16x + x2 = -25 + 64

Combine like terms: -25 + 64 = 39
64 + 16x + x2 = 39

Factor a perfect square on the left side:
(x + 8)(x + 8) = 39

Calculate the square root of the right side: 6.244997998

Break this problem into two subproblems by setting 
(x + 8) equal to 6.244997998 and -6.244997998.


Subproblem 1
x + 8 = 6.244997998

Simplifying
x + 8 = 6.244997998

Reorder the terms:
8 + x = 6.244997998

Solving
8 + x = 6.244997998

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 = 6.244997998 + -8

Combine like terms: 8 + -8 = 0
0 + x = 6.244997998 + -8
x = 6.244997998 + -8

Combine like terms: 6.244997998 + -8 = -1.755002002
x = -1.755002002

Simplifying
x = -1.755002002


Subproblem 2
x + 8 = -6.244997998

Simplifying
x + 8 = -6.244997998

Reorder the terms:
8 + x = -6.244997998

Solving
8 + x = -6.244997998

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 = -6.244997998 + -8

Combine like terms: 8 + -8 = 0
0 + x = -6.244997998 + -8
x = -6.244997998 + -8

Combine like terms: -6.244997998 + -8 = -14.244997998
x = -14.244997998

Simplifying
x = -14.244997998


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.755002002, -14.244997998}

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