(x+3)(x+3)=7

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Solution for (x+3)(x+3)=7 equation:


Simplifying
(x + 3)(x + 3) = 7

Reorder the terms:
(3 + x)(x + 3) = 7

Reorder the terms:
(3 + x)(3 + x) = 7

Multiply (3 + x) * (3 + x)
(3(3 + x) + x(3 + x)) = 7
((3 * 3 + x * 3) + x(3 + x)) = 7
((9 + 3x) + x(3 + x)) = 7
(9 + 3x + (3 * x + x * x)) = 7
(9 + 3x + (3x + x2)) = 7

Combine like terms: 3x + 3x = 6x
(9 + 6x + x2) = 7

Solving
9 + 6x + x2 = 7

Solving for variable 'x'.

Reorder the terms:
9 + -7 + 6x + x2 = 7 + -7

Combine like terms: 9 + -7 = 2
2 + 6x + x2 = 7 + -7

Combine like terms: 7 + -7 = 0
2 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 6x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 6x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 6x + x2 = 0 + -2
6x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
6x + x2 = -2

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -2 + 9

Reorder the terms:
9 + 6x + x2 = -2 + 9

Combine like terms: -2 + 9 = 7
9 + 6x + x2 = 7

Factor a perfect square on the left side:
(x + 3)(x + 3) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + 3) equal to 2.645751311 and -2.645751311.


Subproblem 1
x + 3 = 2.645751311

Simplifying
x + 3 = 2.645751311

Reorder the terms:
3 + x = 2.645751311

Solving
3 + x = 2.645751311

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 2.645751311 + -3

Combine like terms: 3 + -3 = 0
0 + x = 2.645751311 + -3
x = 2.645751311 + -3

Combine like terms: 2.645751311 + -3 = -0.354248689
x = -0.354248689

Simplifying
x = -0.354248689


Subproblem 2
x + 3 = -2.645751311

Simplifying
x + 3 = -2.645751311

Reorder the terms:
3 + x = -2.645751311

Solving
3 + x = -2.645751311

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -2.645751311 + -3

Combine like terms: 3 + -3 = 0
0 + x = -2.645751311 + -3
x = -2.645751311 + -3

Combine like terms: -2.645751311 + -3 = -5.645751311
x = -5.645751311

Simplifying
x = -5.645751311


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.354248689, -5.645751311}

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