(x+2)(x+3)=36

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Solution for (x+2)(x+3)=36 equation:


Simplifying
(x + 2)(x + 3) = 36

Reorder the terms:
(2 + x)(x + 3) = 36

Reorder the terms:
(2 + x)(3 + x) = 36

Multiply (2 + x) * (3 + x)
(2(3 + x) + x(3 + x)) = 36
((3 * 2 + x * 2) + x(3 + x)) = 36
((6 + 2x) + x(3 + x)) = 36
(6 + 2x + (3 * x + x * x)) = 36
(6 + 2x + (3x + x2)) = 36

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2) = 36

Solving
6 + 5x + x2 = 36

Solving for variable 'x'.

Reorder the terms:
6 + -36 + 5x + x2 = 36 + -36

Combine like terms: 6 + -36 = -30
-30 + 5x + x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-30 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 5x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 5x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 5x + x2 = 0 + 30
5x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
5x + x2 = 30

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 30 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 30 + 6.25

Combine like terms: 30 + 6.25 = 36.25
6.25 + 5x + x2 = 36.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(x + 2.5) equal to 6.020797289 and -6.020797289.

Subproblem 1

x + 2.5 = 6.020797289 Simplifying x + 2.5 = 6.020797289 Reorder the terms: 2.5 + x = 6.020797289 Solving 2.5 + x = 6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 6.020797289 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 6.020797289 + -2.5 x = 6.020797289 + -2.5 Combine like terms: 6.020797289 + -2.5 = 3.520797289 x = 3.520797289 Simplifying x = 3.520797289

Subproblem 2

x + 2.5 = -6.020797289 Simplifying x + 2.5 = -6.020797289 Reorder the terms: 2.5 + x = -6.020797289 Solving 2.5 + x = -6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -6.020797289 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -6.020797289 + -2.5 x = -6.020797289 + -2.5 Combine like terms: -6.020797289 + -2.5 = -8.520797289 x = -8.520797289 Simplifying x = -8.520797289

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.520797289, -8.520797289}

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