9x^2-51x-8=0

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Solution for 9x^2-51x-8=0 equation: 


Simplifying
9x2 + -51x + -8 = 0

Reorder the terms:
-8 + -51x + 9x2 = 0

Solving
-8 + -51x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-0.8888888889 + -5.666666667x + x2 = 0

Move the constant term to the right:

Add '0.8888888889' to each side of the equation.
-0.8888888889 + -5.666666667x + 0.8888888889 + x2 = 0 + 0.8888888889

Reorder the terms:
-0.8888888889 + 0.8888888889 + -5.666666667x + x2 = 0 + 0.8888888889

Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000
0.0000000000 + -5.666666667x + x2 = 0 + 0.8888888889
-5.666666667x + x2 = 0 + 0.8888888889

Combine like terms: 0 + 0.8888888889 = 0.8888888889
-5.666666667x + x2 = 0.8888888889

The x term is -5.666666667x.  Take half its coefficient (-2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
-5.666666667x + 8.027777782 + x2 = 0.8888888889 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667x + x2 = 0.8888888889 + 8.027777782

Combine like terms: 0.8888888889 + 8.027777782 = 8.9166666709
8.027777782 + -5.666666667x + x2 = 8.9166666709

Factor a perfect square on the left side:
(x + -2.833333334)(x + -2.833333334) = 8.9166666709

Calculate the square root of the right side: 2.986078812

Break this problem into two subproblems by setting 
(x + -2.833333334) equal to 2.986078812 and -2.986078812.


Subproblem 1
x + -2.833333334 = 2.986078812

Simplifying
x + -2.833333334 = 2.986078812

Reorder the terms:
-2.833333334 + x = 2.986078812

Solving
-2.833333334 + x = 2.986078812

Solving for variable 'x'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + x = 2.986078812 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = 2.986078812 + 2.833333334
x = 2.986078812 + 2.833333334

Combine like terms: 2.986078812 + 2.833333334 = 5.819412146
x = 5.819412146

Simplifying
x = 5.819412146


Subproblem 2
x + -2.833333334 = -2.986078812

Simplifying
x + -2.833333334 = -2.986078812

Reorder the terms:
-2.833333334 + x = -2.986078812

Solving
-2.833333334 + x = -2.986078812

Solving for variable 'x'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + x = -2.986078812 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = -2.986078812 + 2.833333334
x = -2.986078812 + 2.833333334

Combine like terms: -2.986078812 + 2.833333334 = -0.152745478
x = -0.152745478

Simplifying
x = -0.152745478


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.819412146, -0.152745478}

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