3x^2-48x+160=0

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Solution for 3x^2-48x+160=0 equation: 


Simplifying
3x2 + -48x + 160 = 0

Reorder the terms:
160 + -48x + 3x2 = 0

Solving
160 + -48x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
53.33333333 + -16x + x2 = 0

Move the constant term to the right:

Add '-53.33333333' to each side of the equation.
53.33333333 + -16x + -53.33333333 + x2 = 0 + -53.33333333

Reorder the terms:
53.33333333 + -53.33333333 + -16x + x2 = 0 + -53.33333333

Combine like terms: 53.33333333 + -53.33333333 = 0.00000000
0.00000000 + -16x + x2 = 0 + -53.33333333
-16x + x2 = 0 + -53.33333333

Combine like terms: 0 + -53.33333333 = -53.33333333
-16x + x2 = -53.33333333

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 = -53.33333333 + 64

Reorder the terms:
64 + -16x + x2 = -53.33333333 + 64

Combine like terms: -53.33333333 + 64 = 10.66666667
64 + -16x + x2 = 10.66666667

Factor a perfect square on the left side:
(x + -8)(x + -8) = 10.66666667

Calculate the square root of the right side: 3.265986324

Break this problem into two subproblems by setting 
(x + -8) equal to 3.265986324 and -3.265986324.


Subproblem 1
x + -8 = 3.265986324

Simplifying
x + -8 = 3.265986324

Reorder the terms:
-8 + x = 3.265986324

Solving
-8 + x = 3.265986324

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 = 3.265986324 + 8

Combine like terms: -8 + 8 = 0
0 + x = 3.265986324 + 8
x = 3.265986324 + 8

Combine like terms: 3.265986324 + 8 = 11.265986324
x = 11.265986324

Simplifying
x = 11.265986324


Subproblem 2
x + -8 = -3.265986324

Simplifying
x + -8 = -3.265986324

Reorder the terms:
-8 + x = -3.265986324

Solving
-8 + x = -3.265986324

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 = -3.265986324 + 8

Combine like terms: -8 + 8 = 0
0 + x = -3.265986324 + 8
x = -3.265986324 + 8

Combine like terms: -3.265986324 + 8 = 4.734013676
x = 4.734013676

Simplifying
x = 4.734013676


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.265986324, 4.734013676}

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