9x^2-78x-26=0

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Solution for 9x^2-78x-26=0 equation: 


Simplifying
9x2 + -78x + -26 = 0

Reorder the terms:
-26 + -78x + 9x2 = 0

Solving
-26 + -78x + 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'.
-2.888888889 + -8.666666667x + x2 = 0

Move the constant term to the right:

Add '2.888888889' to each side of the equation.
-2.888888889 + -8.666666667x + 2.888888889 + x2 = 0 + 2.888888889

Reorder the terms:
-2.888888889 + 2.888888889 + -8.666666667x + x2 = 0 + 2.888888889

Combine like terms: -2.888888889 + 2.888888889 = 0.000000000
0.000000000 + -8.666666667x + x2 = 0 + 2.888888889
-8.666666667x + x2 = 0 + 2.888888889

Combine like terms: 0 + 2.888888889 = 2.888888889
-8.666666667x + x2 = 2.888888889

The x term is -8.666666667x.  Take half its coefficient (-4.333333334).
Square it (18.77777778) and add it to both sides.

Add '18.77777778' to each side of the equation.
-8.666666667x + 18.77777778 + x2 = 2.888888889 + 18.77777778

Reorder the terms:
18.77777778 + -8.666666667x + x2 = 2.888888889 + 18.77777778

Combine like terms: 2.888888889 + 18.77777778 = 21.666666669
18.77777778 + -8.666666667x + x2 = 21.666666669

Factor a perfect square on the left side:
(x + -4.333333334)(x + -4.333333334) = 21.666666669

Calculate the square root of the right side: 4.654746682

Break this problem into two subproblems by setting 
(x + -4.333333334) equal to 4.654746682 and -4.654746682.


Subproblem 1
x + -4.333333334 = 4.654746682

Simplifying
x + -4.333333334 = 4.654746682

Reorder the terms:
-4.333333334 + x = 4.654746682

Solving
-4.333333334 + x = 4.654746682

Solving for variable 'x'.

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

Add '4.333333334' to each side of the equation.
-4.333333334 + 4.333333334 + x = 4.654746682 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + x = 4.654746682 + 4.333333334
x = 4.654746682 + 4.333333334

Combine like terms: 4.654746682 + 4.333333334 = 8.988080016
x = 8.988080016

Simplifying
x = 8.988080016


Subproblem 2
x + -4.333333334 = -4.654746682

Simplifying
x + -4.333333334 = -4.654746682

Reorder the terms:
-4.333333334 + x = -4.654746682

Solving
-4.333333334 + x = -4.654746682

Solving for variable 'x'.

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

Add '4.333333334' to each side of the equation.
-4.333333334 + 4.333333334 + x = -4.654746682 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + x = -4.654746682 + 4.333333334
x = -4.654746682 + 4.333333334

Combine like terms: -4.654746682 + 4.333333334 = -0.321413348
x = -0.321413348

Simplifying
x = -0.321413348


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.988080016, -0.321413348}

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