(x+7)(x+7)-20=0

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Solution for (x+7)(x+7)-20=0 equation: 


Simplifying
(x + 7)(x + 7) + -20 = 0

Reorder the terms:
(7 + x)(x + 7) + -20 = 0

Reorder the terms:
(7 + x)(7 + x) + -20 = 0

Multiply (7 + x) * (7 + x)
(7(7 + x) + x(7 + x)) + -20 = 0
((7 * 7 + x * 7) + x(7 + x)) + -20 = 0
((49 + 7x) + x(7 + x)) + -20 = 0
(49 + 7x + (7 * x + x * x)) + -20 = 0
(49 + 7x + (7x + x2)) + -20 = 0

Combine like terms: 7x + 7x = 14x
(49 + 14x + x2) + -20 = 0

Reorder the terms:
49 + -20 + 14x + x2 = 0

Combine like terms: 49 + -20 = 29
29 + 14x + x2 = 0

Solving
29 + 14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-29' to each side of the equation.
29 + 14x + -29 + x2 = 0 + -29

Reorder the terms:
29 + -29 + 14x + x2 = 0 + -29

Combine like terms: 29 + -29 = 0
0 + 14x + x2 = 0 + -29
14x + x2 = 0 + -29

Combine like terms: 0 + -29 = -29
14x + x2 = -29

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = -29 + 49

Reorder the terms:
49 + 14x + x2 = -29 + 49

Combine like terms: -29 + 49 = 20
49 + 14x + x2 = 20

Factor a perfect square on the left side:
(x + 7)(x + 7) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(x + 7) equal to 4.472135955 and -4.472135955.


Subproblem 1
x + 7 = 4.472135955

Simplifying
x + 7 = 4.472135955

Reorder the terms:
7 + x = 4.472135955

Solving
7 + x = 4.472135955

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 4.472135955 + -7

Combine like terms: 7 + -7 = 0
0 + x = 4.472135955 + -7
x = 4.472135955 + -7

Combine like terms: 4.472135955 + -7 = -2.527864045
x = -2.527864045

Simplifying
x = -2.527864045


Subproblem 2
x + 7 = -4.472135955

Simplifying
x + 7 = -4.472135955

Reorder the terms:
7 + x = -4.472135955

Solving
7 + x = -4.472135955

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -4.472135955 + -7

Combine like terms: 7 + -7 = 0
0 + x = -4.472135955 + -7
x = -4.472135955 + -7

Combine like terms: -4.472135955 + -7 = -11.472135955
x = -11.472135955

Simplifying
x = -11.472135955


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.527864045, -11.472135955}

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