(x+3)(x+4)=44

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Solution for (x+3)(x+4)=44 equation: 


Simplifying
(x + 3)(x + 4) = 44

Reorder the terms:
(3 + x)(x + 4) = 44

Reorder the terms:
(3 + x)(4 + x) = 44

Multiply (3 + x) * (4 + x)
(3(4 + x) + x(4 + x)) = 44
((4 * 3 + x * 3) + x(4 + x)) = 44
((12 + 3x) + x(4 + x)) = 44
(12 + 3x + (4 * x + x * x)) = 44
(12 + 3x + (4x + x2)) = 44

Combine like terms: 3x + 4x = 7x
(12 + 7x + x2) = 44

Solving
12 + 7x + x2 = 44

Solving for variable 'x'.

Reorder the terms:
12 + -44 + 7x + x2 = 44 + -44

Combine like terms: 12 + -44 = -32
-32 + 7x + x2 = 44 + -44

Combine like terms: 44 + -44 = 0
-32 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 7x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + 7x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 7x + x2 = 0 + 32
7x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
7x + x2 = 32

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 32 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 32 + 12.25

Combine like terms: 32 + 12.25 = 44.25
12.25 + 7x + x2 = 44.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 44.25

Calculate the square root of the right side: 6.652067348

Break this problem into two subproblems by setting 
(x + 3.5) equal to 6.652067348 and -6.652067348.


Subproblem 1
x + 3.5 = 6.652067348

Simplifying
x + 3.5 = 6.652067348

Reorder the terms:
3.5 + x = 6.652067348

Solving
3.5 + x = 6.652067348

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 6.652067348 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 6.652067348 + -3.5
x = 6.652067348 + -3.5

Combine like terms: 6.652067348 + -3.5 = 3.152067348
x = 3.152067348

Simplifying
x = 3.152067348


Subproblem 2
x + 3.5 = -6.652067348

Simplifying
x + 3.5 = -6.652067348

Reorder the terms:
3.5 + x = -6.652067348

Solving
3.5 + x = -6.652067348

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -6.652067348 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -6.652067348 + -3.5
x = -6.652067348 + -3.5

Combine like terms: -6.652067348 + -3.5 = -10.152067348
x = -10.152067348

Simplifying
x = -10.152067348


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.152067348, -10.152067348}

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