x^2-5*x-344=0

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Solution for x^2-5*x-344=0 equation: 


Simplifying
x2 + -5x + -344 = 0

Reorder the terms:
-344 + -5x + x2 = 0

Solving
-344 + -5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '344' to each side of the equation.
-344 + -5x + 344 + x2 = 0 + 344

Reorder the terms:
-344 + 344 + -5x + x2 = 0 + 344

Combine like terms: -344 + 344 = 0
0 + -5x + x2 = 0 + 344
-5x + x2 = 0 + 344

Combine like terms: 0 + 344 = 344
-5x + x2 = 344

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 344 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 344 + 6.25

Combine like terms: 344 + 6.25 = 350.25
6.25 + -5x + x2 = 350.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 350.25

Calculate the square root of the right side: 18.714967272

Break this problem into two subproblems by setting 
(x + -2.5) equal to 18.714967272 and -18.714967272.


Subproblem 1
x + -2.5 = 18.714967272

Simplifying
x + -2.5 = 18.714967272

Reorder the terms:
-2.5 + x = 18.714967272

Solving
-2.5 + x = 18.714967272

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 18.714967272 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 18.714967272 + 2.5
x = 18.714967272 + 2.5

Combine like terms: 18.714967272 + 2.5 = 21.214967272
x = 21.214967272

Simplifying
x = 21.214967272


Subproblem 2
x + -2.5 = -18.714967272

Simplifying
x + -2.5 = -18.714967272

Reorder the terms:
-2.5 + x = -18.714967272

Solving
-2.5 + x = -18.714967272

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -18.714967272 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -18.714967272 + 2.5
x = -18.714967272 + 2.5

Combine like terms: -18.714967272 + 2.5 = -16.214967272
x = -16.214967272

Simplifying
x = -16.214967272


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.214967272, -16.214967272}

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