3x^2-33x+48=0

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Solution for 3x^2-33x+48=0 equation: 


Simplifying
3x2 + -33x + 48 = 0

Reorder the terms:
48 + -33x + 3x2 = 0

Solving
48 + -33x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(16 + -11x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(16 + -11x + x2)' equal to zero and attempt to solve:

Simplifying
16 + -11x + x2 = 0

Solving
16 + -11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -11x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -11x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -11x + x2 = 0 + -16
-11x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-11x + x2 = -16

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = -16 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -16 + 30.25

Combine like terms: -16 + 30.25 = 14.25
30.25 + -11x + x2 = 14.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + -5.5) equal to 3.774917218 and -3.774917218.


Subproblem 1
x + -5.5 = 3.774917218

Simplifying
x + -5.5 = 3.774917218

Reorder the terms:
-5.5 + x = 3.774917218

Solving
-5.5 + x = 3.774917218

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 3.774917218 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 3.774917218 + 5.5
x = 3.774917218 + 5.5

Combine like terms: 3.774917218 + 5.5 = 9.274917218
x = 9.274917218

Simplifying
x = 9.274917218


Subproblem 2
x + -5.5 = -3.774917218

Simplifying
x + -5.5 = -3.774917218

Reorder the terms:
-5.5 + x = -3.774917218

Solving
-5.5 + x = -3.774917218

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -3.774917218 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -3.774917218 + 5.5
x = -3.774917218 + 5.5

Combine like terms: -3.774917218 + 5.5 = 1.725082782
x = 1.725082782

Simplifying
x = 1.725082782


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.274917218, 1.725082782}
Solution
x = {9.274917218, 1.725082782}

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