(x+3)(x+3)=6

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Solution for (x+3)(x+3)=6 equation:


Simplifying
(x + 3)(x + 3) = 6

Reorder the terms:
(3 + x)(x + 3) = 6

Reorder the terms:
(3 + x)(3 + x) = 6

Multiply (3 + x) * (3 + x)
(3(3 + x) + x(3 + x)) = 6
((3 * 3 + x * 3) + x(3 + x)) = 6
((9 + 3x) + x(3 + x)) = 6
(9 + 3x + (3 * x + x * x)) = 6
(9 + 3x + (3x + x2)) = 6

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

Solving
9 + 6x + x2 = 6

Solving for variable 'x'.

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

Combine like terms: 9 + -6 = 3
3 + 6x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
3 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 6x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 6x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 6x + x2 = 0 + -3
6x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
6x + x2 = -3

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 = -3 + 9

Reorder the terms:
9 + 6x + x2 = -3 + 9

Combine like terms: -3 + 9 = 6
9 + 6x + x2 = 6

Factor a perfect square on the left side:
(x + 3)(x + 3) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + 3) equal to 2.449489743 and -2.449489743.

Subproblem 1

x + 3 = 2.449489743 Simplifying x + 3 = 2.449489743 Reorder the terms: 3 + x = 2.449489743 Solving 3 + x = 2.449489743 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 = 2.449489743 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.449489743 + -3 x = 2.449489743 + -3 Combine like terms: 2.449489743 + -3 = -0.550510257 x = -0.550510257 Simplifying x = -0.550510257

Subproblem 2

x + 3 = -2.449489743 Simplifying x + 3 = -2.449489743 Reorder the terms: 3 + x = -2.449489743 Solving 3 + x = -2.449489743 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 = -2.449489743 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.449489743 + -3 x = -2.449489743 + -3 Combine like terms: -2.449489743 + -3 = -5.449489743 x = -5.449489743 Simplifying x = -5.449489743

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.550510257, -5.449489743}

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