4x(2x-9)=23

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Solution for 4x(2x-9)=23 equation: 


Simplifying
4x(2x + -9) = 23

Reorder the terms:
4x(-9 + 2x) = 23
(-9 * 4x + 2x * 4x) = 23
(-36x + 8x2) = 23

Solving
-36x + 8x2 = 23

Solving for variable 'x'.

Reorder the terms:
-23 + -36x + 8x2 = 23 + -23

Combine like terms: 23 + -23 = 0
-23 + -36x + 8x2 = 0

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

Divide each side by '8'.
-2.875 + -4.5x + x2 = 0

Move the constant term to the right:

Add '2.875' to each side of the equation.
-2.875 + -4.5x + 2.875 + x2 = 0 + 2.875

Reorder the terms:
-2.875 + 2.875 + -4.5x + x2 = 0 + 2.875

Combine like terms: -2.875 + 2.875 = 0.000
0.000 + -4.5x + x2 = 0 + 2.875
-4.5x + x2 = 0 + 2.875

Combine like terms: 0 + 2.875 = 2.875
-4.5x + x2 = 2.875

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = 2.875 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 2.875 + 5.0625

Combine like terms: 2.875 + 5.0625 = 7.9375
5.0625 + -4.5x + x2 = 7.9375

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 7.9375

Calculate the square root of the right side: 2.817356917

Break this problem into two subproblems by setting 
(x + -2.25) equal to 2.817356917 and -2.817356917.


Subproblem 1
x + -2.25 = 2.817356917

Simplifying
x + -2.25 = 2.817356917

Reorder the terms:
-2.25 + x = 2.817356917

Solving
-2.25 + x = 2.817356917

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = 2.817356917 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 2.817356917 + 2.25
x = 2.817356917 + 2.25

Combine like terms: 2.817356917 + 2.25 = 5.067356917
x = 5.067356917

Simplifying
x = 5.067356917


Subproblem 2
x + -2.25 = -2.817356917

Simplifying
x + -2.25 = -2.817356917

Reorder the terms:
-2.25 + x = -2.817356917

Solving
-2.25 + x = -2.817356917

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = -2.817356917 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -2.817356917 + 2.25
x = -2.817356917 + 2.25

Combine like terms: -2.817356917 + 2.25 = -0.567356917
x = -0.567356917

Simplifying
x = -0.567356917


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.067356917, -0.567356917}

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