3x^2+19x-51=0

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Solution for 3x^2+19x-51=0 equation: 


Simplifying
3x2 + 19x + -51 = 0

Reorder the terms:
-51 + 19x + 3x2 = 0

Solving
-51 + 19x + 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'.
-17 + 6.333333333x + x2 = 0

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 6.333333333x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + 6.333333333x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 6.333333333x + x2 = 0 + 17
6.333333333x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
6.333333333x + x2 = 17

The x term is 6.333333333x.  Take half its coefficient (3.166666667).
Square it (10.02777778) and add it to both sides.

Add '10.02777778' to each side of the equation.
6.333333333x + 10.02777778 + x2 = 17 + 10.02777778

Reorder the terms:
10.02777778 + 6.333333333x + x2 = 17 + 10.02777778

Combine like terms: 17 + 10.02777778 = 27.02777778
10.02777778 + 6.333333333x + x2 = 27.02777778

Factor a perfect square on the left side:
(x + 3.166666667)(x + 3.166666667) = 27.02777778

Calculate the square root of the right side: 5.198824654

Break this problem into two subproblems by setting 
(x + 3.166666667) equal to 5.198824654 and -5.198824654.


Subproblem 1
x + 3.166666667 = 5.198824654

Simplifying
x + 3.166666667 = 5.198824654

Reorder the terms:
3.166666667 + x = 5.198824654

Solving
3.166666667 + x = 5.198824654

Solving for variable 'x'.

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

Add '-3.166666667' to each side of the equation.
3.166666667 + -3.166666667 + x = 5.198824654 + -3.166666667

Combine like terms: 3.166666667 + -3.166666667 = 0.000000000
0.000000000 + x = 5.198824654 + -3.166666667
x = 5.198824654 + -3.166666667

Combine like terms: 5.198824654 + -3.166666667 = 2.032157987
x = 2.032157987

Simplifying
x = 2.032157987


Subproblem 2
x + 3.166666667 = -5.198824654

Simplifying
x + 3.166666667 = -5.198824654

Reorder the terms:
3.166666667 + x = -5.198824654

Solving
3.166666667 + x = -5.198824654

Solving for variable 'x'.

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

Add '-3.166666667' to each side of the equation.
3.166666667 + -3.166666667 + x = -5.198824654 + -3.166666667

Combine like terms: 3.166666667 + -3.166666667 = 0.000000000
0.000000000 + x = -5.198824654 + -3.166666667
x = -5.198824654 + -3.166666667

Combine like terms: -5.198824654 + -3.166666667 = -8.365491321
x = -8.365491321

Simplifying
x = -8.365491321


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.032157987, -8.365491321}

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