x^2+17x-193=0

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Solution for x^2+17x-193=0 equation: 


Simplifying
x2 + 17x + -193 = 0

Reorder the terms:
-193 + 17x + x2 = 0

Solving
-193 + 17x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '193' to each side of the equation.
-193 + 17x + 193 + x2 = 0 + 193

Reorder the terms:
-193 + 193 + 17x + x2 = 0 + 193

Combine like terms: -193 + 193 = 0
0 + 17x + x2 = 0 + 193
17x + x2 = 0 + 193

Combine like terms: 0 + 193 = 193
17x + x2 = 193

The x term is 17x.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17x + 72.25 + x2 = 193 + 72.25

Reorder the terms:
72.25 + 17x + x2 = 193 + 72.25

Combine like terms: 193 + 72.25 = 265.25
72.25 + 17x + x2 = 265.25

Factor a perfect square on the left side:
(x + 8.5)(x + 8.5) = 265.25

Calculate the square root of the right side: 16.286497475

Break this problem into two subproblems by setting 
(x + 8.5) equal to 16.286497475 and -16.286497475.


Subproblem 1
x + 8.5 = 16.286497475

Simplifying
x + 8.5 = 16.286497475

Reorder the terms:
8.5 + x = 16.286497475

Solving
8.5 + x = 16.286497475

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = 16.286497475 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = 16.286497475 + -8.5
x = 16.286497475 + -8.5

Combine like terms: 16.286497475 + -8.5 = 7.786497475
x = 7.786497475

Simplifying
x = 7.786497475


Subproblem 2
x + 8.5 = -16.286497475

Simplifying
x + 8.5 = -16.286497475

Reorder the terms:
8.5 + x = -16.286497475

Solving
8.5 + x = -16.286497475

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = -16.286497475 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = -16.286497475 + -8.5
x = -16.286497475 + -8.5

Combine like terms: -16.286497475 + -8.5 = -24.786497475
x = -24.786497475

Simplifying
x = -24.786497475


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.786497475, -24.786497475}

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