9x(x-2)-8=14x-7

Solution for 9x(x-2)-8=14x-7 equation:

Simplifying
9x(x + -2) + -8 = 14x + -7

Reorder the terms:
9x(-2 + x) + -8 = 14x + -7
(-2 * 9x + x * 9x) + -8 = 14x + -7
(-18x + 9x2) + -8 = 14x + -7

Reorder the terms:
-8 + -18x + 9x2 = 14x + -7

Reorder the terms:
-8 + -18x + 9x2 = -7 + 14x

Solving
-8 + -18x + 9x2 = -7 + 14x

Solving for variable 'x'.

Reorder the terms:
-8 + 7 + -18x + -14x + 9x2 = -7 + 14x + 7 + -14x

Combine like terms: -8 + 7 = -1
-1 + -18x + -14x + 9x2 = -7 + 14x + 7 + -14x

Combine like terms: -18x + -14x = -32x
-1 + -32x + 9x2 = -7 + 14x + 7 + -14x

Reorder the terms:
-1 + -32x + 9x2 = -7 + 7 + 14x + -14x

Combine like terms: -7 + 7 = 0
-1 + -32x + 9x2 = 0 + 14x + -14x
-1 + -32x + 9x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
-1 + -32x + 9x2 = 0

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

Divide each side by '9'.
-0.1111111111 + -3.555555556x + x2 = 0

Move the constant term to the right:

Add '0.1111111111' to each side of the equation.
-0.1111111111 + -3.555555556x + 0.1111111111 + x2 = 0 + 0.1111111111

Reorder the terms:
-0.1111111111 + 0.1111111111 + -3.555555556x + x2 = 0 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + -3.555555556x + x2 = 0 + 0.1111111111
-3.555555556x + x2 = 0 + 0.1111111111

Combine like terms: 0 + 0.1111111111 = 0.1111111111
-3.555555556x + x2 = 0.1111111111

The x term is -3.555555556x.  Take half its coefficient (-1.777777778).
Square it (3.160493828) and add it to both sides.

Add '3.160493828' to each side of the equation.
-3.555555556x + 3.160493828 + x2 = 0.1111111111 + 3.160493828

Reorder the terms:
3.160493828 + -3.555555556x + x2 = 0.1111111111 + 3.160493828

Combine like terms: 0.1111111111 + 3.160493828 = 3.2716049391
3.160493828 + -3.555555556x + x2 = 3.2716049391

Factor a perfect square on the left side:
(x + -1.777777778)(x + -1.777777778) = 3.2716049391

Calculate the square root of the right side: 1.808757844

Break this problem into two subproblems by setting 
(x + -1.777777778) equal to 1.808757844 and -1.808757844.

Subproblem 1
x + -1.777777778 = 1.808757844

Simplifying
x + -1.777777778 = 1.808757844

Reorder the terms:
-1.777777778 + x = 1.808757844

Solving
-1.777777778 + x = 1.808757844

Solving for variable 'x'.

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

Add '1.777777778' to each side of the equation.
-1.777777778 + 1.777777778 + x = 1.808757844 + 1.777777778

Combine like terms: -1.777777778 + 1.777777778 = 0.000000000
0.000000000 + x = 1.808757844 + 1.777777778
x = 1.808757844 + 1.777777778

Combine like terms: 1.808757844 + 1.777777778 = 3.586535622
x = 3.586535622

Simplifying
x = 3.586535622

Subproblem 2
x + -1.777777778 = -1.808757844

Simplifying
x + -1.777777778 = -1.808757844

Reorder the terms:
-1.777777778 + x = -1.808757844

Solving
-1.777777778 + x = -1.808757844

Solving for variable 'x'.

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

Add '1.777777778' to each side of the equation.
-1.777777778 + 1.777777778 + x = -1.808757844 + 1.777777778

Combine like terms: -1.777777778 + 1.777777778 = 0.000000000
0.000000000 + x = -1.808757844 + 1.777777778
x = -1.808757844 + 1.777777778

Combine like terms: -1.808757844 + 1.777777778 = -0.030980066
x = -0.030980066

Simplifying
x = -0.030980066

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.586535622, -0.030980066}