3x^2+48x-67=0

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Solution for 3x^2+48x-67=0 equation: 


Simplifying
3x2 + 48x + -67 = 0

Reorder the terms:
-67 + 48x + 3x2 = 0

Solving
-67 + 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'.
-22.33333333 + 16x + x2 = 0

Move the constant term to the right:

Add '22.33333333' to each side of the equation.
-22.33333333 + 16x + 22.33333333 + x2 = 0 + 22.33333333

Reorder the terms:
-22.33333333 + 22.33333333 + 16x + x2 = 0 + 22.33333333

Combine like terms: -22.33333333 + 22.33333333 = 0.00000000
0.00000000 + 16x + x2 = 0 + 22.33333333
16x + x2 = 0 + 22.33333333

Combine like terms: 0 + 22.33333333 = 22.33333333
16x + x2 = 22.33333333

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 = 22.33333333 + 64

Reorder the terms:
64 + 16x + x2 = 22.33333333 + 64

Combine like terms: 22.33333333 + 64 = 86.33333333
64 + 16x + x2 = 86.33333333

Factor a perfect square on the left side:
(x + 8)(x + 8) = 86.33333333

Calculate the square root of the right side: 9.291573243

Break this problem into two subproblems by setting 
(x + 8) equal to 9.291573243 and -9.291573243.


Subproblem 1
x + 8 = 9.291573243

Simplifying
x + 8 = 9.291573243

Reorder the terms:
8 + x = 9.291573243

Solving
8 + x = 9.291573243

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 = 9.291573243 + -8

Combine like terms: 8 + -8 = 0
0 + x = 9.291573243 + -8
x = 9.291573243 + -8

Combine like terms: 9.291573243 + -8 = 1.291573243
x = 1.291573243

Simplifying
x = 1.291573243


Subproblem 2
x + 8 = -9.291573243

Simplifying
x + 8 = -9.291573243

Reorder the terms:
8 + x = -9.291573243

Solving
8 + x = -9.291573243

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 = -9.291573243 + -8

Combine like terms: 8 + -8 = 0
0 + x = -9.291573243 + -8
x = -9.291573243 + -8

Combine like terms: -9.291573243 + -8 = -17.291573243
x = -17.291573243

Simplifying
x = -17.291573243


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.291573243, -17.291573243}

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