18x^2-12x-17=0

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Solution for 18x^2-12x-17=0 equation: 


Simplifying
18x2 + -12x + -17 = 0

Reorder the terms:
-17 + -12x + 18x2 = 0

Solving
-17 + -12x + 18x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
18 the coefficient of the squared term: 

Divide each side by '18'.
-0.9444444444 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '0.9444444444' to each side of the equation.
-0.9444444444 + -0.6666666667x + 0.9444444444 + x2 = 0 + 0.9444444444

Reorder the terms:
-0.9444444444 + 0.9444444444 + -0.6666666667x + x2 = 0 + 0.9444444444

Combine like terms: -0.9444444444 + 0.9444444444 = 0.0000000000
0.0000000000 + -0.6666666667x + x2 = 0 + 0.9444444444
-0.6666666667x + x2 = 0 + 0.9444444444

Combine like terms: 0 + 0.9444444444 = 0.9444444444
-0.6666666667x + x2 = 0.9444444444

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = 0.9444444444 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 0.9444444444 + 0.1111111112

Combine like terms: 0.9444444444 + 0.1111111112 = 1.0555555556
0.1111111112 + -0.6666666667x + x2 = 1.0555555556

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 1.0555555556

Calculate the square root of the right side: 1.027402334

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 1.027402334 and -1.027402334.


Subproblem 1
x + -0.3333333334 = 1.027402334

Simplifying
x + -0.3333333334 = 1.027402334

Reorder the terms:
-0.3333333334 + x = 1.027402334

Solving
-0.3333333334 + x = 1.027402334

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = 1.027402334 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = 1.027402334 + 0.3333333334
x = 1.027402334 + 0.3333333334

Combine like terms: 1.027402334 + 0.3333333334 = 1.3607356674
x = 1.3607356674

Simplifying
x = 1.3607356674


Subproblem 2
x + -0.3333333334 = -1.027402334

Simplifying
x + -0.3333333334 = -1.027402334

Reorder the terms:
-0.3333333334 + x = -1.027402334

Solving
-0.3333333334 + x = -1.027402334

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = -1.027402334 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = -1.027402334 + 0.3333333334
x = -1.027402334 + 0.3333333334

Combine like terms: -1.027402334 + 0.3333333334 = -0.6940690006
x = -0.6940690006

Simplifying
x = -0.6940690006


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.3607356674, -0.6940690006}

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