x(x+3)+2x=23

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Solution for x(x+3)+2x=23 equation: 


Simplifying
x(x + 3) + 2x = 23

Reorder the terms:
x(3 + x) + 2x = 23
(3 * x + x * x) + 2x = 23
(3x + x2) + 2x = 23

Reorder the terms:
3x + 2x + x2 = 23

Combine like terms: 3x + 2x = 5x
5x + x2 = 23

Solving
5x + x2 = 23

Solving for variable 'x'.

Reorder the terms:
-23 + 5x + x2 = 23 + -23

Combine like terms: 23 + -23 = 0
-23 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + 5x + 23 + x2 = 0 + 23

Reorder the terms:
-23 + 23 + 5x + x2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + 5x + x2 = 0 + 23
5x + x2 = 0 + 23

Combine like terms: 0 + 23 = 23
5x + x2 = 23

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 23 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 23 + 6.25

Combine like terms: 23 + 6.25 = 29.25
6.25 + 5x + x2 = 29.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 29.25

Calculate the square root of the right side: 5.408326913

Break this problem into two subproblems by setting 
(x + 2.5) equal to 5.408326913 and -5.408326913.


Subproblem 1
x + 2.5 = 5.408326913

Simplifying
x + 2.5 = 5.408326913

Reorder the terms:
2.5 + x = 5.408326913

Solving
2.5 + x = 5.408326913

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 5.408326913 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 5.408326913 + -2.5
x = 5.408326913 + -2.5

Combine like terms: 5.408326913 + -2.5 = 2.908326913
x = 2.908326913

Simplifying
x = 2.908326913


Subproblem 2
x + 2.5 = -5.408326913

Simplifying
x + 2.5 = -5.408326913

Reorder the terms:
2.5 + x = -5.408326913

Solving
2.5 + x = -5.408326913

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -5.408326913 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -5.408326913 + -2.5
x = -5.408326913 + -2.5

Combine like terms: -5.408326913 + -2.5 = -7.908326913
x = -7.908326913

Simplifying
x = -7.908326913


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.908326913, -7.908326913}

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