6x^2-48x+14=0

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Solution for 6x^2-48x+14=0 equation: 


Simplifying
6x2 + -48x + 14 = 0

Reorder the terms:
14 + -48x + 6x2 = 0

Solving
14 + -48x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -24x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + -24x + 3x2)' equal to zero and attempt to solve:

Simplifying
7 + -24x + 3x2 = 0

Solving
7 + -24x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
2.333333333 + -8x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -8x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -8x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -8x + x2 = 0 + -2.333333333
-8x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-8x + x2 = -2.333333333

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 = -2.333333333 + 16

Reorder the terms:
16 + -8x + x2 = -2.333333333 + 16

Combine like terms: -2.333333333 + 16 = 13.666666667
16 + -8x + x2 = 13.666666667

Factor a perfect square on the left side:
(x + -4)(x + -4) = 13.666666667

Calculate the square root of the right side: 3.696845502

Break this problem into two subproblems by setting 
(x + -4) equal to 3.696845502 and -3.696845502.


Subproblem 1
x + -4 = 3.696845502

Simplifying
x + -4 = 3.696845502

Reorder the terms:
-4 + x = 3.696845502

Solving
-4 + x = 3.696845502

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 = 3.696845502 + 4

Combine like terms: -4 + 4 = 0
0 + x = 3.696845502 + 4
x = 3.696845502 + 4

Combine like terms: 3.696845502 + 4 = 7.696845502
x = 7.696845502

Simplifying
x = 7.696845502


Subproblem 2
x + -4 = -3.696845502

Simplifying
x + -4 = -3.696845502

Reorder the terms:
-4 + x = -3.696845502

Solving
-4 + x = -3.696845502

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 = -3.696845502 + 4

Combine like terms: -4 + 4 = 0
0 + x = -3.696845502 + 4
x = -3.696845502 + 4

Combine like terms: -3.696845502 + 4 = 0.303154498
x = 0.303154498

Simplifying
x = 0.303154498


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.696845502, 0.303154498}
Solution
x = {7.696845502, 0.303154498}

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