x^2+34x+68=0

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Solution for x^2+34x+68=0 equation: 


Simplifying
x2 + 34x + 68 = 0

Reorder the terms:
68 + 34x + x2 = 0

Solving
68 + 34x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-68' to each side of the equation.
68 + 34x + -68 + x2 = 0 + -68

Reorder the terms:
68 + -68 + 34x + x2 = 0 + -68

Combine like terms: 68 + -68 = 0
0 + 34x + x2 = 0 + -68
34x + x2 = 0 + -68

Combine like terms: 0 + -68 = -68
34x + x2 = -68

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 = -68 + 289

Reorder the terms:
289 + 34x + x2 = -68 + 289

Combine like terms: -68 + 289 = 221
289 + 34x + x2 = 221

Factor a perfect square on the left side:
(x + 17)(x + 17) = 221

Calculate the square root of the right side: 14.866068747

Break this problem into two subproblems by setting 
(x + 17) equal to 14.866068747 and -14.866068747.


Subproblem 1
x + 17 = 14.866068747

Simplifying
x + 17 = 14.866068747

Reorder the terms:
17 + x = 14.866068747

Solving
17 + x = 14.866068747

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 = 14.866068747 + -17

Combine like terms: 17 + -17 = 0
0 + x = 14.866068747 + -17
x = 14.866068747 + -17

Combine like terms: 14.866068747 + -17 = -2.133931253
x = -2.133931253

Simplifying
x = -2.133931253


Subproblem 2
x + 17 = -14.866068747

Simplifying
x + 17 = -14.866068747

Reorder the terms:
17 + x = -14.866068747

Solving
17 + x = -14.866068747

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 = -14.866068747 + -17

Combine like terms: 17 + -17 = 0
0 + x = -14.866068747 + -17
x = -14.866068747 + -17

Combine like terms: -14.866068747 + -17 = -31.866068747
x = -31.866068747

Simplifying
x = -31.866068747


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.133931253, -31.866068747}

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