x^2-8x-49=0

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Solution for x^2-8x-49=0 equation: 


Simplifying
x2 + -8x + -49 = 0

Reorder the terms:
-49 + -8x + x2 = 0

Solving
-49 + -8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + -8x + 49 + x2 = 0 + 49

Reorder the terms:
-49 + 49 + -8x + x2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + -8x + x2 = 0 + 49
-8x + x2 = 0 + 49

Combine like terms: 0 + 49 = 49
-8x + x2 = 49

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 49 + 16

Reorder the terms:
16 + -8x + x2 = 49 + 16

Combine like terms: 49 + 16 = 65
16 + -8x + x2 = 65

Factor a perfect square on the left side:
(x + -4)(x + -4) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(x + -4) equal to 8.062257748 and -8.062257748.


Subproblem 1
x + -4 = 8.062257748

Simplifying
x + -4 = 8.062257748

Reorder the terms:
-4 + x = 8.062257748

Solving
-4 + x = 8.062257748

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 8.062257748 + 4

Combine like terms: -4 + 4 = 0
0 + x = 8.062257748 + 4
x = 8.062257748 + 4

Combine like terms: 8.062257748 + 4 = 12.062257748
x = 12.062257748

Simplifying
x = 12.062257748


Subproblem 2
x + -4 = -8.062257748

Simplifying
x + -4 = -8.062257748

Reorder the terms:
-4 + x = -8.062257748

Solving
-4 + x = -8.062257748

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -8.062257748 + 4

Combine like terms: -4 + 4 = 0
0 + x = -8.062257748 + 4
x = -8.062257748 + 4

Combine like terms: -8.062257748 + 4 = -4.062257748
x = -4.062257748

Simplifying
x = -4.062257748


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.062257748, -4.062257748}

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