(x+3)(x+3)=10

Solution for (x+3)(x+3)=10 equation:

Simplifying
(x + 3)(x + 3) = 10

Reorder the terms:
(3 + x)(x + 3) = 10

Reorder the terms:
(3 + x)(3 + x) = 10

Multiply (3 + x) * (3 + x)
(3(3 + x) + x(3 + x)) = 10
((3 * 3 + x * 3) + x(3 + x)) = 10
((9 + 3x) + x(3 + x)) = 10
(9 + 3x + (3 * x + x * x)) = 10
(9 + 3x + (3x + x2)) = 10

Combine like terms: 3x + 3x = 6x
(9 + 6x + x2) = 10

Solving
9 + 6x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
9 + -10 + 6x + x2 = 10 + -10

Combine like terms: 9 + -10 = -1
-1 + 6x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-1 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 6x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 6x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 6x + x2 = 0 + 1
6x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
6x + x2 = 1

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 = 1 + 9

Reorder the terms:
9 + 6x + x2 = 1 + 9

Combine like terms: 1 + 9 = 10
9 + 6x + x2 = 10

Factor a perfect square on the left side:
(x + 3)(x + 3) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + 3) equal to 3.16227766 and -3.16227766.

Subproblem 1
x + 3 = 3.16227766

Simplifying
x + 3 = 3.16227766

Reorder the terms:
3 + x = 3.16227766

Solving
3 + x = 3.16227766

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 = 3.16227766 + -3

Combine like terms: 3 + -3 = 0
0 + x = 3.16227766 + -3
x = 3.16227766 + -3

Combine like terms: 3.16227766 + -3 = 0.16227766
x = 0.16227766

Simplifying
x = 0.16227766

Subproblem 2
x + 3 = -3.16227766

Simplifying
x + 3 = -3.16227766

Reorder the terms:
3 + x = -3.16227766

Solving
3 + x = -3.16227766

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 = -3.16227766 + -3

Combine like terms: 3 + -3 = 0
0 + x = -3.16227766 + -3
x = -3.16227766 + -3

Combine like terms: -3.16227766 + -3 = -6.16227766
x = -6.16227766

Simplifying
x = -6.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.16227766, -6.16227766}