9x^2-6x-79=0

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Solution for 9x^2-6x-79=0 equation: 


Simplifying
9x2 + -6x + -79 = 0

Reorder the terms:
-79 + -6x + 9x2 = 0

Solving
-79 + -6x + 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'.
-8.777777778 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '8.777777778' to each side of the equation.
-8.777777778 + -0.6666666667x + 8.777777778 + x2 = 0 + 8.777777778

Reorder the terms:
-8.777777778 + 8.777777778 + -0.6666666667x + x2 = 0 + 8.777777778

Combine like terms: -8.777777778 + 8.777777778 = 0.000000000
0.000000000 + -0.6666666667x + x2 = 0 + 8.777777778
-0.6666666667x + x2 = 0 + 8.777777778

Combine like terms: 0 + 8.777777778 = 8.777777778
-0.6666666667x + x2 = 8.777777778

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 = 8.777777778 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 8.777777778 + 0.1111111112

Combine like terms: 8.777777778 + 0.1111111112 = 8.8888888892
0.1111111112 + -0.6666666667x + x2 = 8.8888888892

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 8.8888888892

Calculate the square root of the right side: 2.98142397

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 2.98142397 and -2.98142397.


Subproblem 1
x + -0.3333333334 = 2.98142397

Simplifying
x + -0.3333333334 = 2.98142397

Reorder the terms:
-0.3333333334 + x = 2.98142397

Solving
-0.3333333334 + x = 2.98142397

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 = 2.98142397 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = 2.98142397 + 0.3333333334
x = 2.98142397 + 0.3333333334

Combine like terms: 2.98142397 + 0.3333333334 = 3.3147573034
x = 3.3147573034

Simplifying
x = 3.3147573034


Subproblem 2
x + -0.3333333334 = -2.98142397

Simplifying
x + -0.3333333334 = -2.98142397

Reorder the terms:
-0.3333333334 + x = -2.98142397

Solving
-0.3333333334 + x = -2.98142397

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 = -2.98142397 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = -2.98142397 + 0.3333333334
x = -2.98142397 + 0.3333333334

Combine like terms: -2.98142397 + 0.3333333334 = -2.6480906366
x = -2.6480906366

Simplifying
x = -2.6480906366


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.3147573034, -2.6480906366}

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