x^2+18x-17=0

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Solution for x^2+18x-17=0 equation: 


Simplifying
x2 + 18x + -17 = 0

Reorder the terms:
-17 + 18x + x2 = 0

Solving
-17 + 18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 18x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + 18x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 18x + x2 = 0 + 17
18x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
18x + x2 = 17

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = 17 + 81

Reorder the terms:
81 + 18x + x2 = 17 + 81

Combine like terms: 17 + 81 = 98
81 + 18x + x2 = 98

Factor a perfect square on the left side:
(x + 9)(x + 9) = 98

Calculate the square root of the right side: 9.899494937

Break this problem into two subproblems by setting 
(x + 9) equal to 9.899494937 and -9.899494937.


Subproblem 1
x + 9 = 9.899494937

Simplifying
x + 9 = 9.899494937

Reorder the terms:
9 + x = 9.899494937

Solving
9 + x = 9.899494937

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = 9.899494937 + -9

Combine like terms: 9 + -9 = 0
0 + x = 9.899494937 + -9
x = 9.899494937 + -9

Combine like terms: 9.899494937 + -9 = 0.899494937
x = 0.899494937

Simplifying
x = 0.899494937


Subproblem 2
x + 9 = -9.899494937

Simplifying
x + 9 = -9.899494937

Reorder the terms:
9 + x = -9.899494937

Solving
9 + x = -9.899494937

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = -9.899494937 + -9

Combine like terms: 9 + -9 = 0
0 + x = -9.899494937 + -9
x = -9.899494937 + -9

Combine like terms: -9.899494937 + -9 = -18.899494937
x = -18.899494937

Simplifying
x = -18.899494937


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.899494937, -18.899494937}

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