-3x^2+18x+1=0

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Solution for -3x^2+18x+1=0 equation: 


Simplifying
-3x2 + 18x + 1 = 0

Reorder the terms:
1 + 18x + -3x2 = 0

Solving
1 + 18x + -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'.
-0.3333333333 + -6x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -6x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -6x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -6x + x2 = 0 + 0.3333333333
-6x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-6x + x2 = 0.3333333333

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 = 0.3333333333 + 9

Reorder the terms:
9 + -6x + x2 = 0.3333333333 + 9

Combine like terms: 0.3333333333 + 9 = 9.3333333333
9 + -6x + x2 = 9.3333333333

Factor a perfect square on the left side:
(x + -3)(x + -3) = 9.3333333333

Calculate the square root of the right side: 3.055050463

Break this problem into two subproblems by setting 
(x + -3) equal to 3.055050463 and -3.055050463.


Subproblem 1
x + -3 = 3.055050463

Simplifying
x + -3 = 3.055050463

Reorder the terms:
-3 + x = 3.055050463

Solving
-3 + x = 3.055050463

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 = 3.055050463 + 3

Combine like terms: -3 + 3 = 0
0 + x = 3.055050463 + 3
x = 3.055050463 + 3

Combine like terms: 3.055050463 + 3 = 6.055050463
x = 6.055050463

Simplifying
x = 6.055050463


Subproblem 2
x + -3 = -3.055050463

Simplifying
x + -3 = -3.055050463

Reorder the terms:
-3 + x = -3.055050463

Solving
-3 + x = -3.055050463

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 = -3.055050463 + 3

Combine like terms: -3 + 3 = 0
0 + x = -3.055050463 + 3
x = -3.055050463 + 3

Combine like terms: -3.055050463 + 3 = -0.055050463
x = -0.055050463

Simplifying
x = -0.055050463


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.055050463, -0.055050463}

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