x^2-34x-18=0

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Solution for x^2-34x-18=0 equation: 


Simplifying
x2 + -34x + -18 = 0

Reorder the terms:
-18 + -34x + x2 = 0

Solving
-18 + -34x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -34x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + -34x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -34x + x2 = 0 + 18
-34x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
-34x + x2 = 18

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 = 18 + 289

Reorder the terms:
289 + -34x + x2 = 18 + 289

Combine like terms: 18 + 289 = 307
289 + -34x + x2 = 307

Factor a perfect square on the left side:
(x + -17)(x + -17) = 307

Calculate the square root of the right side: 17.521415468

Break this problem into two subproblems by setting 
(x + -17) equal to 17.521415468 and -17.521415468.


Subproblem 1
x + -17 = 17.521415468

Simplifying
x + -17 = 17.521415468

Reorder the terms:
-17 + x = 17.521415468

Solving
-17 + x = 17.521415468

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 = 17.521415468 + 17

Combine like terms: -17 + 17 = 0
0 + x = 17.521415468 + 17
x = 17.521415468 + 17

Combine like terms: 17.521415468 + 17 = 34.521415468
x = 34.521415468

Simplifying
x = 34.521415468


Subproblem 2
x + -17 = -17.521415468

Simplifying
x + -17 = -17.521415468

Reorder the terms:
-17 + x = -17.521415468

Solving
-17 + x = -17.521415468

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 = -17.521415468 + 17

Combine like terms: -17 + 17 = 0
0 + x = -17.521415468 + 17
x = -17.521415468 + 17

Combine like terms: -17.521415468 + 17 = -0.521415468
x = -0.521415468

Simplifying
x = -0.521415468


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {34.521415468, -0.521415468}

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