x^2-29x-168=0

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Solution for x^2-29x-168=0 equation: 


Simplifying
x2 + -29x + -168 = 0

Reorder the terms:
-168 + -29x + x2 = 0

Solving
-168 + -29x + 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 + -29x + 168 + x2 = 0 + 168

Reorder the terms:
-168 + 168 + -29x + x2 = 0 + 168

Combine like terms: -168 + 168 = 0
0 + -29x + x2 = 0 + 168
-29x + x2 = 0 + 168

Combine like terms: 0 + 168 = 168
-29x + x2 = 168

The x term is -29x.  Take half its coefficient (-14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
-29x + 210.25 + x2 = 168 + 210.25

Reorder the terms:
210.25 + -29x + x2 = 168 + 210.25

Combine like terms: 168 + 210.25 = 378.25
210.25 + -29x + x2 = 378.25

Factor a perfect square on the left side:
(x + -14.5)(x + -14.5) = 378.25

Calculate the square root of the right side: 19.448650339

Break this problem into two subproblems by setting 
(x + -14.5) equal to 19.448650339 and -19.448650339.


Subproblem 1
x + -14.5 = 19.448650339

Simplifying
x + -14.5 = 19.448650339

Reorder the terms:
-14.5 + x = 19.448650339

Solving
-14.5 + x = 19.448650339

Solving for variable 'x'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + x = 19.448650339 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + x = 19.448650339 + 14.5
x = 19.448650339 + 14.5

Combine like terms: 19.448650339 + 14.5 = 33.948650339
x = 33.948650339

Simplifying
x = 33.948650339


Subproblem 2
x + -14.5 = -19.448650339

Simplifying
x + -14.5 = -19.448650339

Reorder the terms:
-14.5 + x = -19.448650339

Solving
-14.5 + x = -19.448650339

Solving for variable 'x'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + x = -19.448650339 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + x = -19.448650339 + 14.5
x = -19.448650339 + 14.5

Combine like terms: -19.448650339 + 14.5 = -4.948650339
x = -4.948650339

Simplifying
x = -4.948650339


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {33.948650339, -4.948650339}

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