x^2+24x+72=0

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Solution for x^2+24x+72=0 equation:


Simplifying
x2 + 24x + 72 = 0

Reorder the terms:
72 + 24x + x2 = 0

Solving
72 + 24x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-72' to each side of the equation.
72 + 24x + -72 + x2 = 0 + -72

Reorder the terms:
72 + -72 + 24x + x2 = 0 + -72

Combine like terms: 72 + -72 = 0
0 + 24x + x2 = 0 + -72
24x + x2 = 0 + -72

Combine like terms: 0 + -72 = -72
24x + x2 = -72

The x term is 24x.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24x + 144 + x2 = -72 + 144

Reorder the terms:
144 + 24x + x2 = -72 + 144

Combine like terms: -72 + 144 = 72
144 + 24x + x2 = 72

Factor a perfect square on the left side:
(x + 12)(x + 12) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(x + 12) equal to 8.485281374 and -8.485281374.

Subproblem 1

x + 12 = 8.485281374 Simplifying x + 12 = 8.485281374 Reorder the terms: 12 + x = 8.485281374 Solving 12 + x = 8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 8.485281374 + -12 Combine like terms: 12 + -12 = 0 0 + x = 8.485281374 + -12 x = 8.485281374 + -12 Combine like terms: 8.485281374 + -12 = -3.514718626 x = -3.514718626 Simplifying x = -3.514718626

Subproblem 2

x + 12 = -8.485281374 Simplifying x + 12 = -8.485281374 Reorder the terms: 12 + x = -8.485281374 Solving 12 + x = -8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -8.485281374 + -12 Combine like terms: 12 + -12 = 0 0 + x = -8.485281374 + -12 x = -8.485281374 + -12 Combine like terms: -8.485281374 + -12 = -20.485281374 x = -20.485281374 Simplifying x = -20.485281374

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.514718626, -20.485281374}

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