x(x+12)=240

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Solution for x(x+12)=240 equation:


Simplifying
x(x + 12) = 240

Reorder the terms:
x(12 + x) = 240
(12 * x + x * x) = 240
(12x + x2) = 240

Solving
12x + x2 = 240

Solving for variable 'x'.

Reorder the terms:
-240 + 12x + x2 = 240 + -240

Combine like terms: 240 + -240 = 0
-240 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '240' to each side of the equation.
-240 + 12x + 240 + x2 = 0 + 240

Reorder the terms:
-240 + 240 + 12x + x2 = 0 + 240

Combine like terms: -240 + 240 = 0
0 + 12x + x2 = 0 + 240
12x + x2 = 0 + 240

Combine like terms: 0 + 240 = 240
12x + x2 = 240

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 240 + 36

Reorder the terms:
36 + 12x + x2 = 240 + 36

Combine like terms: 240 + 36 = 276
36 + 12x + x2 = 276

Factor a perfect square on the left side:
(x + 6)(x + 6) = 276

Calculate the square root of the right side: 16.613247726

Break this problem into two subproblems by setting 
(x + 6) equal to 16.613247726 and -16.613247726.

Subproblem 1

x + 6 = 16.613247726 Simplifying x + 6 = 16.613247726 Reorder the terms: 6 + x = 16.613247726 Solving 6 + x = 16.613247726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 16.613247726 + -6 Combine like terms: 6 + -6 = 0 0 + x = 16.613247726 + -6 x = 16.613247726 + -6 Combine like terms: 16.613247726 + -6 = 10.613247726 x = 10.613247726 Simplifying x = 10.613247726

Subproblem 2

x + 6 = -16.613247726 Simplifying x + 6 = -16.613247726 Reorder the terms: 6 + x = -16.613247726 Solving 6 + x = -16.613247726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -16.613247726 + -6 Combine like terms: 6 + -6 = 0 0 + x = -16.613247726 + -6 x = -16.613247726 + -6 Combine like terms: -16.613247726 + -6 = -22.613247726 x = -22.613247726 Simplifying x = -22.613247726

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.613247726, -22.613247726}

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