x^2-7x-169=0

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Solution for x^2-7x-169=0 equation: 


Simplifying
x2 + -7x + -169 = 0

Reorder the terms:
-169 + -7x + x2 = 0

Solving
-169 + -7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '169' to each side of the equation.
-169 + -7x + 169 + x2 = 0 + 169

Reorder the terms:
-169 + 169 + -7x + x2 = 0 + 169

Combine like terms: -169 + 169 = 0
0 + -7x + x2 = 0 + 169
-7x + x2 = 0 + 169

Combine like terms: 0 + 169 = 169
-7x + x2 = 169

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 169 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 169 + 12.25

Combine like terms: 169 + 12.25 = 181.25
12.25 + -7x + x2 = 181.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 181.25

Calculate the square root of the right side: 13.462912018

Break this problem into two subproblems by setting 
(x + -3.5) equal to 13.462912018 and -13.462912018.


Subproblem 1
x + -3.5 = 13.462912018

Simplifying
x + -3.5 = 13.462912018

Reorder the terms:
-3.5 + x = 13.462912018

Solving
-3.5 + x = 13.462912018

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 13.462912018 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 13.462912018 + 3.5
x = 13.462912018 + 3.5

Combine like terms: 13.462912018 + 3.5 = 16.962912018
x = 16.962912018

Simplifying
x = 16.962912018


Subproblem 2
x + -3.5 = -13.462912018

Simplifying
x + -3.5 = -13.462912018

Reorder the terms:
-3.5 + x = -13.462912018

Solving
-3.5 + x = -13.462912018

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -13.462912018 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -13.462912018 + 3.5
x = -13.462912018 + 3.5

Combine like terms: -13.462912018 + 3.5 = -9.962912018
x = -9.962912018

Simplifying
x = -9.962912018


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.962912018, -9.962912018}

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