17x^2-64x-169=0

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Solution for 17x^2-64x-169=0 equation:


Simplifying
17x2 + -64x + -169 = 0

Reorder the terms:
-169 + -64x + 17x2 = 0

Solving
-169 + -64x + 17x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
17 the coefficient of the squared term: 

Divide each side by '17'.
-9.941176471 + -3.764705882x + x2 = 0

Move the constant term to the right:

Add '9.941176471' to each side of the equation.
-9.941176471 + -3.764705882x + 9.941176471 + x2 = 0 + 9.941176471

Reorder the terms:
-9.941176471 + 9.941176471 + -3.764705882x + x2 = 0 + 9.941176471

Combine like terms: -9.941176471 + 9.941176471 = 0.000000000
0.000000000 + -3.764705882x + x2 = 0 + 9.941176471
-3.764705882x + x2 = 0 + 9.941176471

Combine like terms: 0 + 9.941176471 = 9.941176471
-3.764705882x + x2 = 9.941176471

The x term is -3.764705882x.  Take half its coefficient (-1.882352941).
Square it (3.543252594) and add it to both sides.

Add '3.543252594' to each side of the equation.
-3.764705882x + 3.543252594 + x2 = 9.941176471 + 3.543252594

Reorder the terms:
3.543252594 + -3.764705882x + x2 = 9.941176471 + 3.543252594

Combine like terms: 9.941176471 + 3.543252594 = 13.484429065
3.543252594 + -3.764705882x + x2 = 13.484429065

Factor a perfect square on the left side:
(x + -1.882352941)(x + -1.882352941) = 13.484429065

Calculate the square root of the right side: 3.672115067

Break this problem into two subproblems by setting 
(x + -1.882352941) equal to 3.672115067 and -3.672115067.


Subproblem 1
x + -1.882352941 = 3.672115067

Simplifying
x + -1.882352941 = 3.672115067

Reorder the terms:
-1.882352941 + x = 3.672115067

Solving
-1.882352941 + x = 3.672115067

Solving for variable 'x'.

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

Add '1.882352941' to each side of the equation.
-1.882352941 + 1.882352941 + x = 3.672115067 + 1.882352941

Combine like terms: -1.882352941 + 1.882352941 = 0.000000000
0.000000000 + x = 3.672115067 + 1.882352941
x = 3.672115067 + 1.882352941

Combine like terms: 3.672115067 + 1.882352941 = 5.554468008
x = 5.554468008

Simplifying
x = 5.554468008


Subproblem 2
x + -1.882352941 = -3.672115067

Simplifying
x + -1.882352941 = -3.672115067

Reorder the terms:
-1.882352941 + x = -3.672115067

Solving
-1.882352941 + x = -3.672115067

Solving for variable 'x'.

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

Add '1.882352941' to each side of the equation.
-1.882352941 + 1.882352941 + x = -3.672115067 + 1.882352941

Combine like terms: -1.882352941 + 1.882352941 = 0.000000000
0.000000000 + x = -3.672115067 + 1.882352941
x = -3.672115067 + 1.882352941

Combine like terms: -3.672115067 + 1.882352941 = -1.789762126
x = -1.789762126

Simplifying
x = -1.789762126


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.554468008, -1.789762126}

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