3x^2+27x-13=0

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Solution for 3x^2+27x-13=0 equation: 


Simplifying
3x2 + 27x + -13 = 0

Reorder the terms:
-13 + 27x + 3x2 = 0

Solving
-13 + 27x + 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 + 9x + x2 = 0

Move the constant term to the right:

Add '4.333333333' to each side of the equation.
-4.333333333 + 9x + 4.333333333 + x2 = 0 + 4.333333333

Reorder the terms:
-4.333333333 + 4.333333333 + 9x + x2 = 0 + 4.333333333

Combine like terms: -4.333333333 + 4.333333333 = 0.000000000
0.000000000 + 9x + x2 = 0 + 4.333333333
9x + x2 = 0 + 4.333333333

Combine like terms: 0 + 4.333333333 = 4.333333333
9x + x2 = 4.333333333

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 4.333333333 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 4.333333333 + 20.25

Combine like terms: 4.333333333 + 20.25 = 24.583333333
20.25 + 9x + x2 = 24.583333333

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 24.583333333

Calculate the square root of the right side: 4.95815826

Break this problem into two subproblems by setting 
(x + 4.5) equal to 4.95815826 and -4.95815826.


Subproblem 1
x + 4.5 = 4.95815826

Simplifying
x + 4.5 = 4.95815826

Reorder the terms:
4.5 + x = 4.95815826

Solving
4.5 + x = 4.95815826

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 4.95815826 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 4.95815826 + -4.5
x = 4.95815826 + -4.5

Combine like terms: 4.95815826 + -4.5 = 0.45815826
x = 0.45815826

Simplifying
x = 0.45815826


Subproblem 2
x + 4.5 = -4.95815826

Simplifying
x + 4.5 = -4.95815826

Reorder the terms:
4.5 + x = -4.95815826

Solving
4.5 + x = -4.95815826

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -4.95815826 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -4.95815826 + -4.5
x = -4.95815826 + -4.5

Combine like terms: -4.95815826 + -4.5 = -9.45815826
x = -9.45815826

Simplifying
x = -9.45815826


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.45815826, -9.45815826}

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