x^2+17x+4=0

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Solution for x^2+17x+4=0 equation: 


Simplifying
x2 + 17x + 4 = 0

Reorder the terms:
4 + 17x + x2 = 0

Solving
4 + 17x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 17x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 17x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 17x + x2 = 0 + -4
17x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
17x + x2 = -4

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 = -4 + 72.25

Reorder the terms:
72.25 + 17x + x2 = -4 + 72.25

Combine like terms: -4 + 72.25 = 68.25
72.25 + 17x + x2 = 68.25

Factor a perfect square on the left side:
(x + 8.5)(x + 8.5) = 68.25

Calculate the square root of the right side: 8.261355821

Break this problem into two subproblems by setting 
(x + 8.5) equal to 8.261355821 and -8.261355821.


Subproblem 1
x + 8.5 = 8.261355821

Simplifying
x + 8.5 = 8.261355821

Reorder the terms:
8.5 + x = 8.261355821

Solving
8.5 + x = 8.261355821

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 = 8.261355821 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = 8.261355821 + -8.5
x = 8.261355821 + -8.5

Combine like terms: 8.261355821 + -8.5 = -0.238644179
x = -0.238644179

Simplifying
x = -0.238644179


Subproblem 2
x + 8.5 = -8.261355821

Simplifying
x + 8.5 = -8.261355821

Reorder the terms:
8.5 + x = -8.261355821

Solving
8.5 + x = -8.261355821

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 = -8.261355821 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = -8.261355821 + -8.5
x = -8.261355821 + -8.5

Combine like terms: -8.261355821 + -8.5 = -16.761355821
x = -16.761355821

Simplifying
x = -16.761355821


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.238644179, -16.761355821}

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