(x+3)(x+3)=48

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Solution for (x+3)(x+3)=48 equation:


Simplifying
(x + 3)(x + 3) = 48

Reorder the terms:
(3 + x)(x + 3) = 48

Reorder the terms:
(3 + x)(3 + x) = 48

Multiply (3 + x) * (3 + x)
(3(3 + x) + x(3 + x)) = 48
((3 * 3 + x * 3) + x(3 + x)) = 48
((9 + 3x) + x(3 + x)) = 48
(9 + 3x + (3 * x + x * x)) = 48
(9 + 3x + (3x + x2)) = 48

Combine like terms: 3x + 3x = 6x
(9 + 6x + x2) = 48

Solving
9 + 6x + x2 = 48

Solving for variable 'x'.

Reorder the terms:
9 + -48 + 6x + x2 = 48 + -48

Combine like terms: 9 + -48 = -39
-39 + 6x + x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-39 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '39' to each side of the equation.
-39 + 6x + 39 + x2 = 0 + 39

Reorder the terms:
-39 + 39 + 6x + x2 = 0 + 39

Combine like terms: -39 + 39 = 0
0 + 6x + x2 = 0 + 39
6x + x2 = 0 + 39

Combine like terms: 0 + 39 = 39
6x + x2 = 39

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 = 39 + 9

Reorder the terms:
9 + 6x + x2 = 39 + 9

Combine like terms: 39 + 9 = 48
9 + 6x + x2 = 48

Factor a perfect square on the left side:
(x + 3)(x + 3) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(x + 3) equal to 6.92820323 and -6.92820323.

Subproblem 1

x + 3 = 6.92820323 Simplifying x + 3 = 6.92820323 Reorder the terms: 3 + x = 6.92820323 Solving 3 + x = 6.92820323 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 = 6.92820323 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.92820323 + -3 x = 6.92820323 + -3 Combine like terms: 6.92820323 + -3 = 3.92820323 x = 3.92820323 Simplifying x = 3.92820323

Subproblem 2

x + 3 = -6.92820323 Simplifying x + 3 = -6.92820323 Reorder the terms: 3 + x = -6.92820323 Solving 3 + x = -6.92820323 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 = -6.92820323 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.92820323 + -3 x = -6.92820323 + -3 Combine like terms: -6.92820323 + -3 = -9.92820323 x = -9.92820323 Simplifying x = -9.92820323

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.92820323, -9.92820323}

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