8x(x-3)=38

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Solution for 8x(x-3)=38 equation: 


Simplifying
8x(x + -3) = 38

Reorder the terms:
8x(-3 + x) = 38
(-3 * 8x + x * 8x) = 38
(-24x + 8x2) = 38

Solving
-24x + 8x2 = 38

Solving for variable 'x'.

Reorder the terms:
-38 + -24x + 8x2 = 38 + -38

Combine like terms: 38 + -38 = 0
-38 + -24x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-19 + -12x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-19 + -12x + 4x2)' equal to zero and attempt to solve:

Simplifying
-19 + -12x + 4x2 = 0

Solving
-19 + -12x + 4x2 = 0

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

Divide each side by '4'.
-4.75 + -3x + x2 = 0

Move the constant term to the right:

Add '4.75' to each side of the equation.
-4.75 + -3x + 4.75 + x2 = 0 + 4.75

Reorder the terms:
-4.75 + 4.75 + -3x + x2 = 0 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + -3x + x2 = 0 + 4.75
-3x + x2 = 0 + 4.75

Combine like terms: 0 + 4.75 = 4.75
-3x + x2 = 4.75

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 4.75 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 4.75 + 2.25

Combine like terms: 4.75 + 2.25 = 7
2.25 + -3x + x2 = 7

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.645751311 and -2.645751311.


Subproblem 1
x + -1.5 = 2.645751311

Simplifying
x + -1.5 = 2.645751311

Reorder the terms:
-1.5 + x = 2.645751311

Solving
-1.5 + x = 2.645751311

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 2.645751311 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2.645751311 + 1.5
x = 2.645751311 + 1.5

Combine like terms: 2.645751311 + 1.5 = 4.145751311
x = 4.145751311

Simplifying
x = 4.145751311


Subproblem 2
x + -1.5 = -2.645751311

Simplifying
x + -1.5 = -2.645751311

Reorder the terms:
-1.5 + x = -2.645751311

Solving
-1.5 + x = -2.645751311

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -2.645751311 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2.645751311 + 1.5
x = -2.645751311 + 1.5

Combine like terms: -2.645751311 + 1.5 = -1.145751311
x = -1.145751311

Simplifying
x = -1.145751311


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.145751311, -1.145751311}
Solution
x = {4.145751311, -1.145751311}

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