3x^2-48x-24=39

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Solution for 3x^2-48x-24=39 equation: 


Simplifying
3x2 + -48x + -24 = 39

Reorder the terms:
-24 + -48x + 3x2 = 39

Solving
-24 + -48x + 3x2 = 39

Solving for variable 'x'.

Reorder the terms:
-24 + -39 + -48x + 3x2 = 39 + -39

Combine like terms: -24 + -39 = -63
-63 + -48x + 3x2 = 39 + -39

Combine like terms: 39 + -39 = 0
-63 + -48x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-21 + -16x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-21 + -16x + x2)' equal to zero and attempt to solve:

Simplifying
-21 + -16x + x2 = 0

Solving
-21 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + -16x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + -16x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -16x + x2 = 0 + 21
-16x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
-16x + x2 = 21

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = 21 + 64

Reorder the terms:
64 + -16x + x2 = 21 + 64

Combine like terms: 21 + 64 = 85
64 + -16x + x2 = 85

Factor a perfect square on the left side:
(x + -8)(x + -8) = 85

Calculate the square root of the right side: 9.219544457

Break this problem into two subproblems by setting 
(x + -8) equal to 9.219544457 and -9.219544457.


Subproblem 1
x + -8 = 9.219544457

Simplifying
x + -8 = 9.219544457

Reorder the terms:
-8 + x = 9.219544457

Solving
-8 + x = 9.219544457

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 9.219544457 + 8

Combine like terms: -8 + 8 = 0
0 + x = 9.219544457 + 8
x = 9.219544457 + 8

Combine like terms: 9.219544457 + 8 = 17.219544457
x = 17.219544457

Simplifying
x = 17.219544457


Subproblem 2
x + -8 = -9.219544457

Simplifying
x + -8 = -9.219544457

Reorder the terms:
-8 + x = -9.219544457

Solving
-8 + x = -9.219544457

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -9.219544457 + 8

Combine like terms: -8 + 8 = 0
0 + x = -9.219544457 + 8
x = -9.219544457 + 8

Combine like terms: -9.219544457 + 8 = -1.219544457
x = -1.219544457

Simplifying
x = -1.219544457


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.219544457, -1.219544457}
Solution
x = {17.219544457, -1.219544457}

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