3x^2-16x-60=0

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Solution for 3x^2-16x-60=0 equation: 


Simplifying
3x2 + -16x + -60 = 0

Reorder the terms:
-60 + -16x + 3x2 = 0

Solving
-60 + -16x + 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'.
-20 + -5.333333333x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -5.333333333x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -5.333333333x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -5.333333333x + x2 = 0 + 20
-5.333333333x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-5.333333333x + x2 = 20

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 = 20 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333x + x2 = 20 + 7.111111113

Combine like terms: 20 + 7.111111113 = 27.111111113
7.111111113 + -5.333333333x + x2 = 27.111111113

Factor a perfect square on the left side:
(x + -2.666666667)(x + -2.666666667) = 27.111111113

Calculate the square root of the right side: 5.206833117

Break this problem into two subproblems by setting 
(x + -2.666666667) equal to 5.206833117 and -5.206833117.


Subproblem 1
x + -2.666666667 = 5.206833117

Simplifying
x + -2.666666667 = 5.206833117

Reorder the terms:
-2.666666667 + x = 5.206833117

Solving
-2.666666667 + x = 5.206833117

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 = 5.206833117 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x = 5.206833117 + 2.666666667
x = 5.206833117 + 2.666666667

Combine like terms: 5.206833117 + 2.666666667 = 7.873499784
x = 7.873499784

Simplifying
x = 7.873499784


Subproblem 2
x + -2.666666667 = -5.206833117

Simplifying
x + -2.666666667 = -5.206833117

Reorder the terms:
-2.666666667 + x = -5.206833117

Solving
-2.666666667 + x = -5.206833117

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 = -5.206833117 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x = -5.206833117 + 2.666666667
x = -5.206833117 + 2.666666667

Combine like terms: -5.206833117 + 2.666666667 = -2.54016645
x = -2.54016645

Simplifying
x = -2.54016645


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.873499784, -2.54016645}

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