2x(x+5)=6+(x+1)

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Solution for 2x(x+5)=6+(x+1) equation: 


Simplifying
2x(x + 5) = 6 + (x + 1)

Reorder the terms:
2x(5 + x) = 6 + (x + 1)
(5 * 2x + x * 2x) = 6 + (x + 1)
(10x + 2x2) = 6 + (x + 1)

Reorder the terms:
10x + 2x2 = 6 + (1 + x)

Remove parenthesis around (1 + x)
10x + 2x2 = 6 + 1 + x

Combine like terms: 6 + 1 = 7
10x + 2x2 = 7 + x

Solving
10x + 2x2 = 7 + x

Solving for variable 'x'.

Reorder the terms:
-7 + 10x + -1x + 2x2 = 7 + x + -7 + -1x

Combine like terms: 10x + -1x = 9x
-7 + 9x + 2x2 = 7 + x + -7 + -1x

Reorder the terms:
-7 + 9x + 2x2 = 7 + -7 + x + -1x

Combine like terms: 7 + -7 = 0
-7 + 9x + 2x2 = 0 + x + -1x
-7 + 9x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-7 + 9x + 2x2 = 0

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

Divide each side by '2'.
-3.5 + 4.5x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 4.5x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 4.5x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 4.5x + x2 = 0 + 3.5
4.5x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
4.5x + x2 = 3.5

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 = 3.5 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 3.5 + 5.0625

Combine like terms: 3.5 + 5.0625 = 8.5625
5.0625 + 4.5x + x2 = 8.5625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 8.5625

Calculate the square root of the right side: 2.926174978

Break this problem into two subproblems by setting 
(x + 2.25) equal to 2.926174978 and -2.926174978.


Subproblem 1
x + 2.25 = 2.926174978

Simplifying
x + 2.25 = 2.926174978

Reorder the terms:
2.25 + x = 2.926174978

Solving
2.25 + x = 2.926174978

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 = 2.926174978 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 2.926174978 + -2.25
x = 2.926174978 + -2.25

Combine like terms: 2.926174978 + -2.25 = 0.676174978
x = 0.676174978

Simplifying
x = 0.676174978


Subproblem 2
x + 2.25 = -2.926174978

Simplifying
x + 2.25 = -2.926174978

Reorder the terms:
2.25 + x = -2.926174978

Solving
2.25 + x = -2.926174978

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 = -2.926174978 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -2.926174978 + -2.25
x = -2.926174978 + -2.25

Combine like terms: -2.926174978 + -2.25 = -5.176174978
x = -5.176174978

Simplifying
x = -5.176174978


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.676174978, -5.176174978}

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