-3x^2-3x+13=0

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Solution for -3x^2-3x+13=0 equation: 


Simplifying
-3x2 + -3x + 13 = 0

Reorder the terms:
13 + -3x + -3x2 = 0

Solving
13 + -3x + -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'.
-4.333333333 + x + x2 = 0

Move the constant term to the right:

Add '4.333333333' to each side of the equation.
-4.333333333 + x + 4.333333333 + x2 = 0 + 4.333333333

Reorder the terms:
-4.333333333 + 4.333333333 + x + x2 = 0 + 4.333333333

Combine like terms: -4.333333333 + 4.333333333 = 0.000000000
0.000000000 + x + x2 = 0 + 4.333333333
x + x2 = 0 + 4.333333333

Combine like terms: 0 + 4.333333333 = 4.333333333
x + x2 = 4.333333333

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 4.333333333 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 4.333333333 + 0.25

Combine like terms: 4.333333333 + 0.25 = 4.583333333
1.25 + x2 = 4.583333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 4.583333333

Calculate the square root of the right side: 2.140872096

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.140872096 and -2.140872096.


Subproblem 1
x + 0.5 = 2.140872096

Simplifying
x + 0.5 = 2.140872096

Reorder the terms:
0.5 + x = 2.140872096

Solving
0.5 + x = 2.140872096

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 2.140872096 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.140872096 + -0.5
x = 2.140872096 + -0.5

Combine like terms: 2.140872096 + -0.5 = 1.640872096
x = 1.640872096

Simplifying
x = 1.640872096


Subproblem 2
x + 0.5 = -2.140872096

Simplifying
x + 0.5 = -2.140872096

Reorder the terms:
0.5 + x = -2.140872096

Solving
0.5 + x = -2.140872096

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -2.140872096 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.140872096 + -0.5
x = -2.140872096 + -0.5

Combine like terms: -2.140872096 + -0.5 = -2.640872096
x = -2.640872096

Simplifying
x = -2.640872096


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.640872096, -2.640872096}

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