(x+12)(x)=576

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Solution for (x+12)(x)=576 equation:


Simplifying
(x + 12)(x) = 576

Reorder the terms:
(12 + x)(x) = 576

Reorder the terms for easier multiplication:
x(12 + x) = 576
(12 * x + x * x) = 576
(12x + x2) = 576

Solving
12x + x2 = 576

Solving for variable 'x'.

Reorder the terms:
-576 + 12x + x2 = 576 + -576

Combine like terms: 576 + -576 = 0
-576 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '576' to each side of the equation.
-576 + 12x + 576 + x2 = 0 + 576

Reorder the terms:
-576 + 576 + 12x + x2 = 0 + 576

Combine like terms: -576 + 576 = 0
0 + 12x + x2 = 0 + 576
12x + x2 = 0 + 576

Combine like terms: 0 + 576 = 576
12x + x2 = 576

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 = 576 + 36

Reorder the terms:
36 + 12x + x2 = 576 + 36

Combine like terms: 576 + 36 = 612
36 + 12x + x2 = 612

Factor a perfect square on the left side:
(x + 6)(x + 6) = 612

Calculate the square root of the right side: 24.738633754

Break this problem into two subproblems by setting 
(x + 6) equal to 24.738633754 and -24.738633754.

Subproblem 1

x + 6 = 24.738633754 Simplifying x + 6 = 24.738633754 Reorder the terms: 6 + x = 24.738633754 Solving 6 + x = 24.738633754 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 = 24.738633754 + -6 Combine like terms: 6 + -6 = 0 0 + x = 24.738633754 + -6 x = 24.738633754 + -6 Combine like terms: 24.738633754 + -6 = 18.738633754 x = 18.738633754 Simplifying x = 18.738633754

Subproblem 2

x + 6 = -24.738633754 Simplifying x + 6 = -24.738633754 Reorder the terms: 6 + x = -24.738633754 Solving 6 + x = -24.738633754 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 = -24.738633754 + -6 Combine like terms: 6 + -6 = 0 0 + x = -24.738633754 + -6 x = -24.738633754 + -6 Combine like terms: -24.738633754 + -6 = -30.738633754 x = -30.738633754 Simplifying x = -30.738633754

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.738633754, -30.738633754}

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