x^2-4x-71=0

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Solution for x^2-4x-71=0 equation: 


Simplifying
x2 + -4x + -71 = 0

Reorder the terms:
-71 + -4x + x2 = 0

Solving
-71 + -4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '71' to each side of the equation.
-71 + -4x + 71 + x2 = 0 + 71

Reorder the terms:
-71 + 71 + -4x + x2 = 0 + 71

Combine like terms: -71 + 71 = 0
0 + -4x + x2 = 0 + 71
-4x + x2 = 0 + 71

Combine like terms: 0 + 71 = 71
-4x + x2 = 71

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 = 71 + 4

Reorder the terms:
4 + -4x + x2 = 71 + 4

Combine like terms: 71 + 4 = 75
4 + -4x + x2 = 75

Factor a perfect square on the left side:
(x + -2)(x + -2) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(x + -2) equal to 8.660254038 and -8.660254038.


Subproblem 1
x + -2 = 8.660254038

Simplifying
x + -2 = 8.660254038

Reorder the terms:
-2 + x = 8.660254038

Solving
-2 + x = 8.660254038

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 = 8.660254038 + 2

Combine like terms: -2 + 2 = 0
0 + x = 8.660254038 + 2
x = 8.660254038 + 2

Combine like terms: 8.660254038 + 2 = 10.660254038
x = 10.660254038

Simplifying
x = 10.660254038


Subproblem 2
x + -2 = -8.660254038

Simplifying
x + -2 = -8.660254038

Reorder the terms:
-2 + x = -8.660254038

Solving
-2 + x = -8.660254038

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 = -8.660254038 + 2

Combine like terms: -2 + 2 = 0
0 + x = -8.660254038 + 2
x = -8.660254038 + 2

Combine like terms: -8.660254038 + 2 = -6.660254038
x = -6.660254038

Simplifying
x = -6.660254038


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.660254038, -6.660254038}

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