9x^2-48x+14=0

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Solution for 9x^2-48x+14=0 equation: 


Simplifying
9x2 + -48x + 14 = 0

Reorder the terms:
14 + -48x + 9x2 = 0

Solving
14 + -48x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
1.555555556 + -5.333333333x + x2 = 0

Move the constant term to the right:

Add '-1.555555556' to each side of the equation.
1.555555556 + -5.333333333x + -1.555555556 + x2 = 0 + -1.555555556

Reorder the terms:
1.555555556 + -1.555555556 + -5.333333333x + x2 = 0 + -1.555555556

Combine like terms: 1.555555556 + -1.555555556 = 0.000000000
0.000000000 + -5.333333333x + x2 = 0 + -1.555555556
-5.333333333x + x2 = 0 + -1.555555556

Combine like terms: 0 + -1.555555556 = -1.555555556
-5.333333333x + x2 = -1.555555556

The x term is -5.333333333x.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333x + 7.111111113 + x2 = -1.555555556 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333x + x2 = -1.555555556 + 7.111111113

Combine like terms: -1.555555556 + 7.111111113 = 5.555555557
7.111111113 + -5.333333333x + x2 = 5.555555557

Factor a perfect square on the left side:
(x + -2.666666667)(x + -2.666666667) = 5.555555557

Calculate the square root of the right side: 2.357022604

Break this problem into two subproblems by setting 
(x + -2.666666667) equal to 2.357022604 and -2.357022604.


Subproblem 1
x + -2.666666667 = 2.357022604

Simplifying
x + -2.666666667 = 2.357022604

Reorder the terms:
-2.666666667 + x = 2.357022604

Solving
-2.666666667 + x = 2.357022604

Solving for variable 'x'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + x = 2.357022604 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x = 2.357022604 + 2.666666667
x = 2.357022604 + 2.666666667

Combine like terms: 2.357022604 + 2.666666667 = 5.023689271
x = 5.023689271

Simplifying
x = 5.023689271


Subproblem 2
x + -2.666666667 = -2.357022604

Simplifying
x + -2.666666667 = -2.357022604

Reorder the terms:
-2.666666667 + x = -2.357022604

Solving
-2.666666667 + x = -2.357022604

Solving for variable 'x'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + x = -2.357022604 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x = -2.357022604 + 2.666666667
x = -2.357022604 + 2.666666667

Combine like terms: -2.357022604 + 2.666666667 = 0.309644063
x = 0.309644063

Simplifying
x = 0.309644063


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.023689271, 0.309644063}

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