(x+4)(x+7)=20

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Solution for (x+4)(x+7)=20 equation:


Simplifying
(x + 4)(x + 7) = 20

Reorder the terms:
(4 + x)(x + 7) = 20

Reorder the terms:
(4 + x)(7 + x) = 20

Multiply (4 + x) * (7 + x)
(4(7 + x) + x(7 + x)) = 20
((7 * 4 + x * 4) + x(7 + x)) = 20
((28 + 4x) + x(7 + x)) = 20
(28 + 4x + (7 * x + x * x)) = 20
(28 + 4x + (7x + x2)) = 20

Combine like terms: 4x + 7x = 11x
(28 + 11x + x2) = 20

Solving
28 + 11x + x2 = 20

Solving for variable 'x'.

Reorder the terms:
28 + -20 + 11x + x2 = 20 + -20

Combine like terms: 28 + -20 = 8
8 + 11x + x2 = 20 + -20

Combine like terms: 20 + -20 = 0
8 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 11x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + 11x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 11x + x2 = 0 + -8
11x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
11x + x2 = -8

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = -8 + 30.25

Reorder the terms:
30.25 + 11x + x2 = -8 + 30.25

Combine like terms: -8 + 30.25 = 22.25
30.25 + 11x + x2 = 22.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(x + 5.5) equal to 4.716990566 and -4.716990566.


Subproblem 1
x + 5.5 = 4.716990566

Simplifying
x + 5.5 = 4.716990566

Reorder the terms:
5.5 + x = 4.716990566

Solving
5.5 + x = 4.716990566

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 4.716990566 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 4.716990566 + -5.5
x = 4.716990566 + -5.5

Combine like terms: 4.716990566 + -5.5 = -0.783009434
x = -0.783009434

Simplifying
x = -0.783009434


Subproblem 2
x + 5.5 = -4.716990566

Simplifying
x + 5.5 = -4.716990566

Reorder the terms:
5.5 + x = -4.716990566

Solving
5.5 + x = -4.716990566

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -4.716990566 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -4.716990566 + -5.5
x = -4.716990566 + -5.5

Combine like terms: -4.716990566 + -5.5 = -10.216990566
x = -10.216990566

Simplifying
x = -10.216990566


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.783009434, -10.216990566}

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