x^2-34x-344=0

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Solution for x^2-34x-344=0 equation: 


Simplifying
x2 + -34x + -344 = 0

Reorder the terms:
-344 + -34x + x2 = 0

Solving
-344 + -34x + 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 + -34x + 344 + x2 = 0 + 344

Reorder the terms:
-344 + 344 + -34x + x2 = 0 + 344

Combine like terms: -344 + 344 = 0
0 + -34x + x2 = 0 + 344
-34x + x2 = 0 + 344

Combine like terms: 0 + 344 = 344
-34x + x2 = 344

The x term is -34x.  Take half its coefficient (-17).
Square it (289) and add it to both sides.

Add '289' to each side of the equation.
-34x + 289 + x2 = 344 + 289

Reorder the terms:
289 + -34x + x2 = 344 + 289

Combine like terms: 344 + 289 = 633
289 + -34x + x2 = 633

Factor a perfect square on the left side:
(x + -17)(x + -17) = 633

Calculate the square root of the right side: 25.159491251

Break this problem into two subproblems by setting 
(x + -17) equal to 25.159491251 and -25.159491251.


Subproblem 1
x + -17 = 25.159491251

Simplifying
x + -17 = 25.159491251

Reorder the terms:
-17 + x = 25.159491251

Solving
-17 + x = 25.159491251

Solving for variable 'x'.

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

Add '17' to each side of the equation.
-17 + 17 + x = 25.159491251 + 17

Combine like terms: -17 + 17 = 0
0 + x = 25.159491251 + 17
x = 25.159491251 + 17

Combine like terms: 25.159491251 + 17 = 42.159491251
x = 42.159491251

Simplifying
x = 42.159491251


Subproblem 2
x + -17 = -25.159491251

Simplifying
x + -17 = -25.159491251

Reorder the terms:
-17 + x = -25.159491251

Solving
-17 + x = -25.159491251

Solving for variable 'x'.

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

Add '17' to each side of the equation.
-17 + 17 + x = -25.159491251 + 17

Combine like terms: -17 + 17 = 0
0 + x = -25.159491251 + 17
x = -25.159491251 + 17

Combine like terms: -25.159491251 + 17 = -8.159491251
x = -8.159491251

Simplifying
x = -8.159491251


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {42.159491251, -8.159491251}

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