x^2+15x+16=0

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Solution for x^2+15x+16=0 equation: 


Simplifying
x2 + 15x + 16 = 0

Reorder the terms:
16 + 15x + x2 = 0

Solving
16 + 15x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 15x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + 15x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 15x + x2 = 0 + -16
15x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
15x + x2 = -16

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = -16 + 56.25

Reorder the terms:
56.25 + 15x + x2 = -16 + 56.25

Combine like terms: -16 + 56.25 = 40.25
56.25 + 15x + x2 = 40.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(x + 7.5) equal to 6.34428877 and -6.34428877.


Subproblem 1
x + 7.5 = 6.34428877

Simplifying
x + 7.5 = 6.34428877

Reorder the terms:
7.5 + x = 6.34428877

Solving
7.5 + x = 6.34428877

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = 6.34428877 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 6.34428877 + -7.5
x = 6.34428877 + -7.5

Combine like terms: 6.34428877 + -7.5 = -1.15571123
x = -1.15571123

Simplifying
x = -1.15571123


Subproblem 2
x + 7.5 = -6.34428877

Simplifying
x + 7.5 = -6.34428877

Reorder the terms:
7.5 + x = -6.34428877

Solving
7.5 + x = -6.34428877

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = -6.34428877 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -6.34428877 + -7.5
x = -6.34428877 + -7.5

Combine like terms: -6.34428877 + -7.5 = -13.84428877
x = -13.84428877

Simplifying
x = -13.84428877


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.15571123, -13.84428877}

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