(x+9)(x+9)=71

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Solution for (x+9)(x+9)=71 equation: 


Simplifying
(x + 9)(x + 9) = 71

Reorder the terms:
(9 + x)(x + 9) = 71

Reorder the terms:
(9 + x)(9 + x) = 71

Multiply (9 + x) * (9 + x)
(9(9 + x) + x(9 + x)) = 71
((9 * 9 + x * 9) + x(9 + x)) = 71
((81 + 9x) + x(9 + x)) = 71
(81 + 9x + (9 * x + x * x)) = 71
(81 + 9x + (9x + x2)) = 71

Combine like terms: 9x + 9x = 18x
(81 + 18x + x2) = 71

Solving
81 + 18x + x2 = 71

Solving for variable 'x'.

Reorder the terms:
81 + -71 + 18x + x2 = 71 + -71

Combine like terms: 81 + -71 = 10
10 + 18x + x2 = 71 + -71

Combine like terms: 71 + -71 = 0
10 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 18x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + 18x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 18x + x2 = 0 + -10
18x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
18x + x2 = -10

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = -10 + 81

Reorder the terms:
81 + 18x + x2 = -10 + 81

Combine like terms: -10 + 81 = 71
81 + 18x + x2 = 71

Factor a perfect square on the left side:
(x + 9)(x + 9) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(x + 9) equal to 8.426149773 and -8.426149773.


Subproblem 1
x + 9 = 8.426149773

Simplifying
x + 9 = 8.426149773

Reorder the terms:
9 + x = 8.426149773

Solving
9 + x = 8.426149773

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = 8.426149773 + -9

Combine like terms: 9 + -9 = 0
0 + x = 8.426149773 + -9
x = 8.426149773 + -9

Combine like terms: 8.426149773 + -9 = -0.573850227
x = -0.573850227

Simplifying
x = -0.573850227


Subproblem 2
x + 9 = -8.426149773

Simplifying
x + 9 = -8.426149773

Reorder the terms:
9 + x = -8.426149773

Solving
9 + x = -8.426149773

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = -8.426149773 + -9

Combine like terms: 9 + -9 = 0
0 + x = -8.426149773 + -9
x = -8.426149773 + -9

Combine like terms: -8.426149773 + -9 = -17.426149773
x = -17.426149773

Simplifying
x = -17.426149773


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.573850227, -17.426149773}

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