49=x(x+9)+(x+4)

Solution for 49=x(x+9)+(x+4) equation:

Simplifying
49 = x(x + 9) + (x + 4)

Reorder the terms:
49 = x(9 + x) + (x + 4)
49 = (9 * x + x * x) + (x + 4)
49 = (9x + x2) + (x + 4)

Reorder the terms:
49 = 9x + x2 + (4 + x)

Remove parenthesis around (4 + x)
49 = 9x + x2 + 4 + x

Reorder the terms:
49 = 4 + 9x + x + x2

Combine like terms: 9x + x = 10x
49 = 4 + 10x + x2

Solving
49 = 4 + 10x + x2

Solving for variable 'x'.

Combine like terms: 49 + -4 = 45
45 + -10x + -1x2 = 4 + 10x + x2 + -4 + -10x + -1x2

Reorder the terms:
45 + -10x + -1x2 = 4 + -4 + 10x + -10x + x2 + -1x2

Combine like terms: 4 + -4 = 0
45 + -10x + -1x2 = 0 + 10x + -10x + x2 + -1x2
45 + -10x + -1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
45 + -10x + -1x2 = 0 + x2 + -1x2
45 + -10x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
45 + -10x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-45 + 10x + x2 = 0

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 10x + 45 + x2 = 0 + 45

Reorder the terms:
-45 + 45 + 10x + x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 10x + x2 = 0 + 45
10x + x2 = 0 + 45

Combine like terms: 0 + 45 = 45
10x + x2 = 45

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 45 + 25

Reorder the terms:
25 + 10x + x2 = 45 + 25

Combine like terms: 45 + 25 = 70
25 + 10x + x2 = 70

Factor a perfect square on the left side:
(x + 5)(x + 5) = 70

Calculate the square root of the right side: 8.366600265

Break this problem into two subproblems by setting 
(x + 5) equal to 8.366600265 and -8.366600265.

Subproblem 1
x + 5 = 8.366600265

Simplifying
x + 5 = 8.366600265

Reorder the terms:
5 + x = 8.366600265

Solving
5 + x = 8.366600265

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 8.366600265 + -5

Combine like terms: 5 + -5 = 0
0 + x = 8.366600265 + -5
x = 8.366600265 + -5

Combine like terms: 8.366600265 + -5 = 3.366600265
x = 3.366600265

Simplifying
x = 3.366600265

Subproblem 2
x + 5 = -8.366600265

Simplifying
x + 5 = -8.366600265

Reorder the terms:
5 + x = -8.366600265

Solving
5 + x = -8.366600265

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -8.366600265 + -5

Combine like terms: 5 + -5 = 0
0 + x = -8.366600265 + -5
x = -8.366600265 + -5

Combine like terms: -8.366600265 + -5 = -13.366600265
x = -13.366600265

Simplifying
x = -13.366600265

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.366600265, -13.366600265}