x^2-4x-65=0

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Solution for x^2-4x-65=0 equation: 


Simplifying
x2 + -4x + -65 = 0

Reorder the terms:
-65 + -4x + x2 = 0

Solving
-65 + -4x + 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 + -4x + 65 + x2 = 0 + 65

Reorder the terms:
-65 + 65 + -4x + x2 = 0 + 65

Combine like terms: -65 + 65 = 0
0 + -4x + x2 = 0 + 65
-4x + x2 = 0 + 65

Combine like terms: 0 + 65 = 65
-4x + x2 = 65

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 65 + 4

Reorder the terms:
4 + -4x + x2 = 65 + 4

Combine like terms: 65 + 4 = 69
4 + -4x + x2 = 69

Factor a perfect square on the left side:
(x + -2)(x + -2) = 69

Calculate the square root of the right side: 8.306623863

Break this problem into two subproblems by setting 
(x + -2) equal to 8.306623863 and -8.306623863.


Subproblem 1
x + -2 = 8.306623863

Simplifying
x + -2 = 8.306623863

Reorder the terms:
-2 + x = 8.306623863

Solving
-2 + x = 8.306623863

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 8.306623863 + 2

Combine like terms: -2 + 2 = 0
0 + x = 8.306623863 + 2
x = 8.306623863 + 2

Combine like terms: 8.306623863 + 2 = 10.306623863
x = 10.306623863

Simplifying
x = 10.306623863


Subproblem 2
x + -2 = -8.306623863

Simplifying
x + -2 = -8.306623863

Reorder the terms:
-2 + x = -8.306623863

Solving
-2 + x = -8.306623863

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -8.306623863 + 2

Combine like terms: -2 + 2 = 0
0 + x = -8.306623863 + 2
x = -8.306623863 + 2

Combine like terms: -8.306623863 + 2 = -6.306623863
x = -6.306623863

Simplifying
x = -6.306623863


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.306623863, -6.306623863}

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