x^2+24x+99=0

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Solution for x^2+24x+99=0 equation:


Simplifying
x2 + 24x + 99 = 0

Reorder the terms:
99 + 24x + x2 = 0

Solving
99 + 24x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-99' to each side of the equation.
99 + 24x + -99 + x2 = 0 + -99

Reorder the terms:
99 + -99 + 24x + x2 = 0 + -99

Combine like terms: 99 + -99 = 0
0 + 24x + x2 = 0 + -99
24x + x2 = 0 + -99

Combine like terms: 0 + -99 = -99
24x + x2 = -99

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 = -99 + 144

Reorder the terms:
144 + 24x + x2 = -99 + 144

Combine like terms: -99 + 144 = 45
144 + 24x + x2 = 45

Factor a perfect square on the left side:
(x + 12)(x + 12) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(x + 12) equal to 6.708203933 and -6.708203933.

Subproblem 1

x + 12 = 6.708203933 Simplifying x + 12 = 6.708203933 Reorder the terms: 12 + x = 6.708203933 Solving 12 + x = 6.708203933 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 = 6.708203933 + -12 Combine like terms: 12 + -12 = 0 0 + x = 6.708203933 + -12 x = 6.708203933 + -12 Combine like terms: 6.708203933 + -12 = -5.291796067 x = -5.291796067 Simplifying x = -5.291796067

Subproblem 2

x + 12 = -6.708203933 Simplifying x + 12 = -6.708203933 Reorder the terms: 12 + x = -6.708203933 Solving 12 + x = -6.708203933 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 = -6.708203933 + -12 Combine like terms: 12 + -12 = 0 0 + x = -6.708203933 + -12 x = -6.708203933 + -12 Combine like terms: -6.708203933 + -12 = -18.708203933 x = -18.708203933 Simplifying x = -18.708203933

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-5.291796067, -18.708203933}

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