(x+7)(x+7)=18

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Solution for (x+7)(x+7)=18 equation: 


Simplifying
(x + 7)(x + 7) = 18

Reorder the terms:
(7 + x)(x + 7) = 18

Reorder the terms:
(7 + x)(7 + x) = 18

Multiply (7 + x) * (7 + x)
(7(7 + x) + x(7 + x)) = 18
((7 * 7 + x * 7) + x(7 + x)) = 18
((49 + 7x) + x(7 + x)) = 18
(49 + 7x + (7 * x + x * x)) = 18
(49 + 7x + (7x + x2)) = 18

Combine like terms: 7x + 7x = 14x
(49 + 14x + x2) = 18

Solving
49 + 14x + x2 = 18

Solving for variable 'x'.

Reorder the terms:
49 + -18 + 14x + x2 = 18 + -18

Combine like terms: 49 + -18 = 31
31 + 14x + x2 = 18 + -18

Combine like terms: 18 + -18 = 0
31 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-31' to each side of the equation.
31 + 14x + -31 + x2 = 0 + -31

Reorder the terms:
31 + -31 + 14x + x2 = 0 + -31

Combine like terms: 31 + -31 = 0
0 + 14x + x2 = 0 + -31
14x + x2 = 0 + -31

Combine like terms: 0 + -31 = -31
14x + x2 = -31

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 = -31 + 49

Reorder the terms:
49 + 14x + x2 = -31 + 49

Combine like terms: -31 + 49 = 18
49 + 14x + x2 = 18

Factor a perfect square on the left side:
(x + 7)(x + 7) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + 7) equal to 4.242640687 and -4.242640687.


Subproblem 1
x + 7 = 4.242640687

Simplifying
x + 7 = 4.242640687

Reorder the terms:
7 + x = 4.242640687

Solving
7 + x = 4.242640687

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 = 4.242640687 + -7

Combine like terms: 7 + -7 = 0
0 + x = 4.242640687 + -7
x = 4.242640687 + -7

Combine like terms: 4.242640687 + -7 = -2.757359313
x = -2.757359313

Simplifying
x = -2.757359313


Subproblem 2
x + 7 = -4.242640687

Simplifying
x + 7 = -4.242640687

Reorder the terms:
7 + x = -4.242640687

Solving
7 + x = -4.242640687

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 = -4.242640687 + -7

Combine like terms: 7 + -7 = 0
0 + x = -4.242640687 + -7
x = -4.242640687 + -7

Combine like terms: -4.242640687 + -7 = -11.242640687
x = -11.242640687

Simplifying
x = -11.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.757359313, -11.242640687}

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