x^2-39x-248=0

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Solution for x^2-39x-248=0 equation: 


Simplifying
x2 + -39x + -248 = 0

Reorder the terms:
-248 + -39x + x2 = 0

Solving
-248 + -39x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '248' to each side of the equation.
-248 + -39x + 248 + x2 = 0 + 248

Reorder the terms:
-248 + 248 + -39x + x2 = 0 + 248

Combine like terms: -248 + 248 = 0
0 + -39x + x2 = 0 + 248
-39x + x2 = 0 + 248

Combine like terms: 0 + 248 = 248
-39x + x2 = 248

The x term is -39x.  Take half its coefficient (-19.5).
Square it (380.25) and add it to both sides.

Add '380.25' to each side of the equation.
-39x + 380.25 + x2 = 248 + 380.25

Reorder the terms:
380.25 + -39x + x2 = 248 + 380.25

Combine like terms: 248 + 380.25 = 628.25
380.25 + -39x + x2 = 628.25

Factor a perfect square on the left side:
(x + -19.5)(x + -19.5) = 628.25

Calculate the square root of the right side: 25.064915719

Break this problem into two subproblems by setting 
(x + -19.5) equal to 25.064915719 and -25.064915719.


Subproblem 1
x + -19.5 = 25.064915719

Simplifying
x + -19.5 = 25.064915719

Reorder the terms:
-19.5 + x = 25.064915719

Solving
-19.5 + x = 25.064915719

Solving for variable 'x'.

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

Add '19.5' to each side of the equation.
-19.5 + 19.5 + x = 25.064915719 + 19.5

Combine like terms: -19.5 + 19.5 = 0.0
0.0 + x = 25.064915719 + 19.5
x = 25.064915719 + 19.5

Combine like terms: 25.064915719 + 19.5 = 44.564915719
x = 44.564915719

Simplifying
x = 44.564915719


Subproblem 2
x + -19.5 = -25.064915719

Simplifying
x + -19.5 = -25.064915719

Reorder the terms:
-19.5 + x = -25.064915719

Solving
-19.5 + x = -25.064915719

Solving for variable 'x'.

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

Add '19.5' to each side of the equation.
-19.5 + 19.5 + x = -25.064915719 + 19.5

Combine like terms: -19.5 + 19.5 = 0.0
0.0 + x = -25.064915719 + 19.5
x = -25.064915719 + 19.5

Combine like terms: -25.064915719 + 19.5 = -5.564915719
x = -5.564915719

Simplifying
x = -5.564915719


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {44.564915719, -5.564915719}

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