x^2-4x-73=0

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Solution for x^2-4x-73=0 equation:


Simplifying
x2 + -4x + -73 = 0

Reorder the terms:
-73 + -4x + x2 = 0

Solving
-73 + -4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '73' to each side of the equation.
-73 + -4x + 73 + x2 = 0 + 73

Reorder the terms:
-73 + 73 + -4x + x2 = 0 + 73

Combine like terms: -73 + 73 = 0
0 + -4x + x2 = 0 + 73
-4x + x2 = 0 + 73

Combine like terms: 0 + 73 = 73
-4x + x2 = 73

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 = 73 + 4

Reorder the terms:
4 + -4x + x2 = 73 + 4

Combine like terms: 73 + 4 = 77
4 + -4x + x2 = 77

Factor a perfect square on the left side:
(x + -2)(x + -2) = 77

Calculate the square root of the right side: 8.774964387

Break this problem into two subproblems by setting 
(x + -2) equal to 8.774964387 and -8.774964387.


Subproblem 1
x + -2 = 8.774964387

Simplifying
x + -2 = 8.774964387

Reorder the terms:
-2 + x = 8.774964387

Solving
-2 + x = 8.774964387

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 = 8.774964387 + 2

Combine like terms: -2 + 2 = 0
0 + x = 8.774964387 + 2
x = 8.774964387 + 2

Combine like terms: 8.774964387 + 2 = 10.774964387
x = 10.774964387

Simplifying
x = 10.774964387


Subproblem 2
x + -2 = -8.774964387

Simplifying
x + -2 = -8.774964387

Reorder the terms:
-2 + x = -8.774964387

Solving
-2 + x = -8.774964387

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 = -8.774964387 + 2

Combine like terms: -2 + 2 = 0
0 + x = -8.774964387 + 2
x = -8.774964387 + 2

Combine like terms: -8.774964387 + 2 = -6.774964387
x = -6.774964387

Simplifying
x = -6.774964387


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.774964387, -6.774964387}

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