3x^2+18x-51=0

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Solution for 3x^2+18x-51=0 equation: 


Simplifying
3x2 + 18x + -51 = 0

Reorder the terms:
-51 + 18x + 3x2 = 0

Solving
-51 + 18x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-17 + 6x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-17 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
-17 + 6x + x2 = 0

Solving
-17 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 6x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + 6x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 6x + x2 = 0 + 17
6x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
6x + x2 = 17

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 17 + 9

Reorder the terms:
9 + 6x + x2 = 17 + 9

Combine like terms: 17 + 9 = 26
9 + 6x + x2 = 26

Factor a perfect square on the left side:
(x + 3)(x + 3) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(x + 3) equal to 5.099019514 and -5.099019514.


Subproblem 1
x + 3 = 5.099019514

Simplifying
x + 3 = 5.099019514

Reorder the terms:
3 + x = 5.099019514

Solving
3 + x = 5.099019514

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 5.099019514 + -3

Combine like terms: 3 + -3 = 0
0 + x = 5.099019514 + -3
x = 5.099019514 + -3

Combine like terms: 5.099019514 + -3 = 2.099019514
x = 2.099019514

Simplifying
x = 2.099019514


Subproblem 2
x + 3 = -5.099019514

Simplifying
x + 3 = -5.099019514

Reorder the terms:
3 + x = -5.099019514

Solving
3 + x = -5.099019514

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -5.099019514 + -3

Combine like terms: 3 + -3 = 0
0 + x = -5.099019514 + -3
x = -5.099019514 + -3

Combine like terms: -5.099019514 + -3 = -8.099019514
x = -8.099019514

Simplifying
x = -8.099019514


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.099019514, -8.099019514}
Solution
x = {2.099019514, -8.099019514}

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