3x^2-24x-243=0

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Solution for 3x^2-24x-243=0 equation: 


Simplifying
3x2 + -24x + -243 = 0

Reorder the terms:
-243 + -24x + 3x2 = 0

Solving
-243 + -24x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-81 + -8x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-81 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
-81 + -8x + x2 = 0

Solving
-81 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '81' to each side of the equation.
-81 + -8x + 81 + x2 = 0 + 81

Reorder the terms:
-81 + 81 + -8x + x2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + -8x + x2 = 0 + 81
-8x + x2 = 0 + 81

Combine like terms: 0 + 81 = 81
-8x + x2 = 81

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 81 + 16

Reorder the terms:
16 + -8x + x2 = 81 + 16

Combine like terms: 81 + 16 = 97
16 + -8x + x2 = 97

Factor a perfect square on the left side:
(x + -4)(x + -4) = 97

Calculate the square root of the right side: 9.848857802

Break this problem into two subproblems by setting 
(x + -4) equal to 9.848857802 and -9.848857802.


Subproblem 1
x + -4 = 9.848857802

Simplifying
x + -4 = 9.848857802

Reorder the terms:
-4 + x = 9.848857802

Solving
-4 + x = 9.848857802

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + x = 9.848857802 + 4

Combine like terms: -4 + 4 = 0
0 + x = 9.848857802 + 4
x = 9.848857802 + 4

Combine like terms: 9.848857802 + 4 = 13.848857802
x = 13.848857802

Simplifying
x = 13.848857802


Subproblem 2
x + -4 = -9.848857802

Simplifying
x + -4 = -9.848857802

Reorder the terms:
-4 + x = -9.848857802

Solving
-4 + x = -9.848857802

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + x = -9.848857802 + 4

Combine like terms: -4 + 4 = 0
0 + x = -9.848857802 + 4
x = -9.848857802 + 4

Combine like terms: -9.848857802 + 4 = -5.848857802
x = -5.848857802

Simplifying
x = -5.848857802


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.848857802, -5.848857802}
Solution
x = {13.848857802, -5.848857802}

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