x^2+21x-192=0

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Solution for x^2+21x-192=0 equation: 


Simplifying
x2 + 21x + -192 = 0

Reorder the terms:
-192 + 21x + x2 = 0

Solving
-192 + 21x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '192' to each side of the equation.
-192 + 21x + 192 + x2 = 0 + 192

Reorder the terms:
-192 + 192 + 21x + x2 = 0 + 192

Combine like terms: -192 + 192 = 0
0 + 21x + x2 = 0 + 192
21x + x2 = 0 + 192

Combine like terms: 0 + 192 = 192
21x + x2 = 192

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = 192 + 110.25

Reorder the terms:
110.25 + 21x + x2 = 192 + 110.25

Combine like terms: 192 + 110.25 = 302.25
110.25 + 21x + x2 = 302.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 302.25

Calculate the square root of the right side: 17.385338651

Break this problem into two subproblems by setting 
(x + 10.5) equal to 17.385338651 and -17.385338651.


Subproblem 1
x + 10.5 = 17.385338651

Simplifying
x + 10.5 = 17.385338651

Reorder the terms:
10.5 + x = 17.385338651

Solving
10.5 + x = 17.385338651

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = 17.385338651 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 17.385338651 + -10.5
x = 17.385338651 + -10.5

Combine like terms: 17.385338651 + -10.5 = 6.885338651
x = 6.885338651

Simplifying
x = 6.885338651


Subproblem 2
x + 10.5 = -17.385338651

Simplifying
x + 10.5 = -17.385338651

Reorder the terms:
10.5 + x = -17.385338651

Solving
10.5 + x = -17.385338651

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = -17.385338651 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -17.385338651 + -10.5
x = -17.385338651 + -10.5

Combine like terms: -17.385338651 + -10.5 = -27.885338651
x = -27.885338651

Simplifying
x = -27.885338651


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.885338651, -27.885338651}

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