x^2+17x+32=0

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Solution for x^2+17x+32=0 equation: 


Simplifying
x2 + 17x + 32 = 0

Reorder the terms:
32 + 17x + x2 = 0

Solving
32 + 17x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + 17x + -32 + x2 = 0 + -32

Reorder the terms:
32 + -32 + 17x + x2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + 17x + x2 = 0 + -32
17x + x2 = 0 + -32

Combine like terms: 0 + -32 = -32
17x + x2 = -32

The x term is 17x.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17x + 72.25 + x2 = -32 + 72.25

Reorder the terms:
72.25 + 17x + x2 = -32 + 72.25

Combine like terms: -32 + 72.25 = 40.25
72.25 + 17x + x2 = 40.25

Factor a perfect square on the left side:
(x + 8.5)(x + 8.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(x + 8.5) equal to 6.34428877 and -6.34428877.


Subproblem 1
x + 8.5 = 6.34428877

Simplifying
x + 8.5 = 6.34428877

Reorder the terms:
8.5 + x = 6.34428877

Solving
8.5 + x = 6.34428877

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = 6.34428877 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = 6.34428877 + -8.5
x = 6.34428877 + -8.5

Combine like terms: 6.34428877 + -8.5 = -2.15571123
x = -2.15571123

Simplifying
x = -2.15571123


Subproblem 2
x + 8.5 = -6.34428877

Simplifying
x + 8.5 = -6.34428877

Reorder the terms:
8.5 + x = -6.34428877

Solving
8.5 + x = -6.34428877

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = -6.34428877 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = -6.34428877 + -8.5
x = -6.34428877 + -8.5

Combine like terms: -6.34428877 + -8.5 = -14.84428877
x = -14.84428877

Simplifying
x = -14.84428877


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.15571123, -14.84428877}

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