9x^2-8x-7=0

Solution for 9x^2-8x-7=0 equation:

Simplifying
9x2 + -8x + -7 = 0

Reorder the terms:
-7 + -8x + 9x2 = 0

Solving
-7 + -8x + 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'.
-0.7777777778 + -0.8888888889x + x2 = 0

Move the constant term to the right:

Add '0.7777777778' to each side of the equation.
-0.7777777778 + -0.8888888889x + 0.7777777778 + x2 = 0 + 0.7777777778

Reorder the terms:
-0.7777777778 + 0.7777777778 + -0.8888888889x + x2 = 0 + 0.7777777778

Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000
0.0000000000 + -0.8888888889x + x2 = 0 + 0.7777777778
-0.8888888889x + x2 = 0 + 0.7777777778

Combine like terms: 0 + 0.7777777778 = 0.7777777778
-0.8888888889x + x2 = 0.7777777778

The x term is -0.8888888889x.  Take half its coefficient (-0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
-0.8888888889x + 0.1975308642 + x2 = 0.7777777778 + 0.1975308642

Reorder the terms:
0.1975308642 + -0.8888888889x + x2 = 0.7777777778 + 0.1975308642

Combine like terms: 0.7777777778 + 0.1975308642 = 0.975308642
0.1975308642 + -0.8888888889x + x2 = 0.975308642

Factor a perfect square on the left side:
(x + -0.4444444445)(x + -0.4444444445) = 0.975308642

Calculate the square root of the right side: 0.987577157

Break this problem into two subproblems by setting 
(x + -0.4444444445) equal to 0.987577157 and -0.987577157.

Subproblem 1
x + -0.4444444445 = 0.987577157

Simplifying
x + -0.4444444445 = 0.987577157

Reorder the terms:
-0.4444444445 + x = 0.987577157

Solving
-0.4444444445 + x = 0.987577157

Solving for variable 'x'.

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

Add '0.4444444445' to each side of the equation.
-0.4444444445 + 0.4444444445 + x = 0.987577157 + 0.4444444445

Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000
0.0000000000 + x = 0.987577157 + 0.4444444445
x = 0.987577157 + 0.4444444445

Combine like terms: 0.987577157 + 0.4444444445 = 1.4320216015
x = 1.4320216015

Simplifying
x = 1.4320216015

Subproblem 2
x + -0.4444444445 = -0.987577157

Simplifying
x + -0.4444444445 = -0.987577157

Reorder the terms:
-0.4444444445 + x = -0.987577157

Solving
-0.4444444445 + x = -0.987577157

Solving for variable 'x'.

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

Add '0.4444444445' to each side of the equation.
-0.4444444445 + 0.4444444445 + x = -0.987577157 + 0.4444444445

Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000
0.0000000000 + x = -0.987577157 + 0.4444444445
x = -0.987577157 + 0.4444444445

Combine like terms: -0.987577157 + 0.4444444445 = -0.5431327125
x = -0.5431327125

Simplifying
x = -0.5431327125

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.4320216015, -0.5431327125}