144=(12+x)*(8+x)

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Solution for 144=(12+x)*(8+x) equation:


Simplifying
144 = (12 + x)(8 + x)

Multiply (12 + x) * (8 + x)
144 = (12(8 + x) + x(8 + x))
144 = ((8 * 12 + x * 12) + x(8 + x))
144 = ((96 + 12x) + x(8 + x))
144 = (96 + 12x + (8 * x + x * x))
144 = (96 + 12x + (8x + x2))

Combine like terms: 12x + 8x = 20x
144 = (96 + 20x + x2)

Solving
144 = 96 + 20x + x2

Solving for variable 'x'.

Combine like terms: 144 + -96 = 48
48 + -20x + -1x2 = 96 + 20x + x2 + -96 + -20x + -1x2

Reorder the terms:
48 + -20x + -1x2 = 96 + -96 + 20x + -20x + x2 + -1x2

Combine like terms: 96 + -96 = 0
48 + -20x + -1x2 = 0 + 20x + -20x + x2 + -1x2
48 + -20x + -1x2 = 20x + -20x + x2 + -1x2

Combine like terms: 20x + -20x = 0
48 + -20x + -1x2 = 0 + x2 + -1x2
48 + -20x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
48 + -20x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-48 + 20x + x2 = 0

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 20x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + 20x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 20x + x2 = 0 + 48
20x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
20x + x2 = 48

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 48 + 100

Reorder the terms:
100 + 20x + x2 = 48 + 100

Combine like terms: 48 + 100 = 148
100 + 20x + x2 = 148

Factor a perfect square on the left side:
(x + 10)(x + 10) = 148

Calculate the square root of the right side: 12.165525061

Break this problem into two subproblems by setting 
(x + 10) equal to 12.165525061 and -12.165525061.

Subproblem 1

x + 10 = 12.165525061 Simplifying x + 10 = 12.165525061 Reorder the terms: 10 + x = 12.165525061 Solving 10 + x = 12.165525061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 12.165525061 + -10 Combine like terms: 10 + -10 = 0 0 + x = 12.165525061 + -10 x = 12.165525061 + -10 Combine like terms: 12.165525061 + -10 = 2.165525061 x = 2.165525061 Simplifying x = 2.165525061

Subproblem 2

x + 10 = -12.165525061 Simplifying x + 10 = -12.165525061 Reorder the terms: 10 + x = -12.165525061 Solving 10 + x = -12.165525061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -12.165525061 + -10 Combine like terms: 10 + -10 = 0 0 + x = -12.165525061 + -10 x = -12.165525061 + -10 Combine like terms: -12.165525061 + -10 = -22.165525061 x = -22.165525061 Simplifying x = -22.165525061

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.165525061, -22.165525061}

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