x^2+34x-168=0

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Solution for x^2+34x-168=0 equation: 


Simplifying
x2 + 34x + -168 = 0

Reorder the terms:
-168 + 34x + x2 = 0

Solving
-168 + 34x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '168' to each side of the equation.
-168 + 34x + 168 + x2 = 0 + 168

Reorder the terms:
-168 + 168 + 34x + x2 = 0 + 168

Combine like terms: -168 + 168 = 0
0 + 34x + x2 = 0 + 168
34x + x2 = 0 + 168

Combine like terms: 0 + 168 = 168
34x + x2 = 168

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 = 168 + 289

Reorder the terms:
289 + 34x + x2 = 168 + 289

Combine like terms: 168 + 289 = 457
289 + 34x + x2 = 457

Factor a perfect square on the left side:
(x + 17)(x + 17) = 457

Calculate the square root of the right side: 21.377558326

Break this problem into two subproblems by setting 
(x + 17) equal to 21.377558326 and -21.377558326.


Subproblem 1
x + 17 = 21.377558326

Simplifying
x + 17 = 21.377558326

Reorder the terms:
17 + x = 21.377558326

Solving
17 + x = 21.377558326

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 = 21.377558326 + -17

Combine like terms: 17 + -17 = 0
0 + x = 21.377558326 + -17
x = 21.377558326 + -17

Combine like terms: 21.377558326 + -17 = 4.377558326
x = 4.377558326

Simplifying
x = 4.377558326


Subproblem 2
x + 17 = -21.377558326

Simplifying
x + 17 = -21.377558326

Reorder the terms:
17 + x = -21.377558326

Solving
17 + x = -21.377558326

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 = -21.377558326 + -17

Combine like terms: 17 + -17 = 0
0 + x = -21.377558326 + -17
x = -21.377558326 + -17

Combine like terms: -21.377558326 + -17 = -38.377558326
x = -38.377558326

Simplifying
x = -38.377558326


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.377558326, -38.377558326}

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