x^2-7x-65=0

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Solution for x^2-7x-65=0 equation: 


Simplifying
x2 + -7x + -65 = 0

Reorder the terms:
-65 + -7x + x2 = 0

Solving
-65 + -7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '65' to each side of the equation.
-65 + -7x + 65 + x2 = 0 + 65

Reorder the terms:
-65 + 65 + -7x + x2 = 0 + 65

Combine like terms: -65 + 65 = 0
0 + -7x + x2 = 0 + 65
-7x + x2 = 0 + 65

Combine like terms: 0 + 65 = 65
-7x + x2 = 65

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 = 65 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 65 + 12.25

Combine like terms: 65 + 12.25 = 77.25
12.25 + -7x + x2 = 77.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 77.25

Calculate the square root of the right side: 8.789197916

Break this problem into two subproblems by setting 
(x + -3.5) equal to 8.789197916 and -8.789197916.


Subproblem 1
x + -3.5 = 8.789197916

Simplifying
x + -3.5 = 8.789197916

Reorder the terms:
-3.5 + x = 8.789197916

Solving
-3.5 + x = 8.789197916

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 = 8.789197916 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 8.789197916 + 3.5
x = 8.789197916 + 3.5

Combine like terms: 8.789197916 + 3.5 = 12.289197916
x = 12.289197916

Simplifying
x = 12.289197916


Subproblem 2
x + -3.5 = -8.789197916

Simplifying
x + -3.5 = -8.789197916

Reorder the terms:
-3.5 + x = -8.789197916

Solving
-3.5 + x = -8.789197916

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 = -8.789197916 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -8.789197916 + 3.5
x = -8.789197916 + 3.5

Combine like terms: -8.789197916 + 3.5 = -5.289197916
x = -5.289197916

Simplifying
x = -5.289197916


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.289197916, -5.289197916}

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