5x(x-23)=37

Solution for 5x(x-23)=37 equation:

Simplifying
5x(x + -23) = 37

Reorder the terms:
5x(-23 + x) = 37
(-23 * 5x + x * 5x) = 37
(-115x + 5x2) = 37

Solving
-115x + 5x2 = 37

Solving for variable 'x'.

Reorder the terms:
-37 + -115x + 5x2 = 37 + -37

Combine like terms: 37 + -37 = 0
-37 + -115x + 5x2 = 0

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

Divide each side by '5'.
-7.4 + -23x + x2 = 0

Move the constant term to the right:

Add '7.4' to each side of the equation.
-7.4 + -23x + 7.4 + x2 = 0 + 7.4

Reorder the terms:
-7.4 + 7.4 + -23x + x2 = 0 + 7.4

Combine like terms: -7.4 + 7.4 = 0.0
0.0 + -23x + x2 = 0 + 7.4
-23x + x2 = 0 + 7.4

Combine like terms: 0 + 7.4 = 7.4
-23x + x2 = 7.4

The x term is -23x.  Take half its coefficient (-11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
-23x + 132.25 + x2 = 7.4 + 132.25

Reorder the terms:
132.25 + -23x + x2 = 7.4 + 132.25

Combine like terms: 7.4 + 132.25 = 139.65
132.25 + -23x + x2 = 139.65

Factor a perfect square on the left side:
(x + -11.5)(x + -11.5) = 139.65

Calculate the square root of the right side: 11.817360111

Break this problem into two subproblems by setting 
(x + -11.5) equal to 11.817360111 and -11.817360111.

Subproblem 1
x + -11.5 = 11.817360111

Simplifying
x + -11.5 = 11.817360111

Reorder the terms:
-11.5 + x = 11.817360111

Solving
-11.5 + x = 11.817360111

Solving for variable 'x'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + x = 11.817360111 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + x = 11.817360111 + 11.5
x = 11.817360111 + 11.5

Combine like terms: 11.817360111 + 11.5 = 23.317360111
x = 23.317360111

Simplifying
x = 23.317360111

Subproblem 2
x + -11.5 = -11.817360111

Simplifying
x + -11.5 = -11.817360111

Reorder the terms:
-11.5 + x = -11.817360111

Solving
-11.5 + x = -11.817360111

Solving for variable 'x'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + x = -11.817360111 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + x = -11.817360111 + 11.5
x = -11.817360111 + 11.5

Combine like terms: -11.817360111 + 11.5 = -0.317360111
x = -0.317360111

Simplifying
x = -0.317360111

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.317360111, -0.317360111}