x^2-78x-304=0

Solution for x^2-78x-304=0 equation:

Simplifying
x2 + -78x + -304 = 0

Reorder the terms:
-304 + -78x + x2 = 0

Solving
-304 + -78x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '304' to each side of the equation.
-304 + -78x + 304 + x2 = 0 + 304

Reorder the terms:
-304 + 304 + -78x + x2 = 0 + 304

Combine like terms: -304 + 304 = 0
0 + -78x + x2 = 0 + 304
-78x + x2 = 0 + 304

Combine like terms: 0 + 304 = 304
-78x + x2 = 304

The x term is -78x.  Take half its coefficient (-39).
Square it (1521) and add it to both sides.

Add '1521' to each side of the equation.
-78x + 1521 + x2 = 304 + 1521

Reorder the terms:
1521 + -78x + x2 = 304 + 1521

Combine like terms: 304 + 1521 = 1825
1521 + -78x + x2 = 1825

Factor a perfect square on the left side:
(x + -39)(x + -39) = 1825

Calculate the square root of the right side: 42.720018727

Break this problem into two subproblems by setting 
(x + -39) equal to 42.720018727 and -42.720018727.

Subproblem 1
x + -39 = 42.720018727

Simplifying
x + -39 = 42.720018727

Reorder the terms:
-39 + x = 42.720018727

Solving
-39 + x = 42.720018727

Solving for variable 'x'.

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

Add '39' to each side of the equation.
-39 + 39 + x = 42.720018727 + 39

Combine like terms: -39 + 39 = 0
0 + x = 42.720018727 + 39
x = 42.720018727 + 39

Combine like terms: 42.720018727 + 39 = 81.720018727
x = 81.720018727

Simplifying
x = 81.720018727

Subproblem 2
x + -39 = -42.720018727

Simplifying
x + -39 = -42.720018727

Reorder the terms:
-39 + x = -42.720018727

Solving
-39 + x = -42.720018727

Solving for variable 'x'.

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

Add '39' to each side of the equation.
-39 + 39 + x = -42.720018727 + 39

Combine like terms: -39 + 39 = 0
0 + x = -42.720018727 + 39
x = -42.720018727 + 39

Combine like terms: -42.720018727 + 39 = -3.720018727
x = -3.720018727

Simplifying
x = -3.720018727

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {81.720018727, -3.720018727}