3x^2+23x-2=0

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Solution for 3x^2+23x-2=0 equation: 


Simplifying
3x2 + 23x + -2 = 0

Reorder the terms:
-2 + 23x + 3x2 = 0

Solving
-2 + 23x + 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'.
-0.6666666667 + 7.666666667x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 7.666666667x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 7.666666667x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 7.666666667x + x2 = 0 + 0.6666666667
7.666666667x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
7.666666667x + x2 = 0.6666666667

The x term is 7.666666667x.  Take half its coefficient (3.833333334).
Square it (14.69444445) and add it to both sides.

Add '14.69444445' to each side of the equation.
7.666666667x + 14.69444445 + x2 = 0.6666666667 + 14.69444445

Reorder the terms:
14.69444445 + 7.666666667x + x2 = 0.6666666667 + 14.69444445

Combine like terms: 0.6666666667 + 14.69444445 = 15.3611111167
14.69444445 + 7.666666667x + x2 = 15.3611111167

Factor a perfect square on the left side:
(x + 3.833333334)(x + 3.833333334) = 15.3611111167

Calculate the square root of the right side: 3.919325339

Break this problem into two subproblems by setting 
(x + 3.833333334) equal to 3.919325339 and -3.919325339.


Subproblem 1
x + 3.833333334 = 3.919325339

Simplifying
x + 3.833333334 = 3.919325339

Reorder the terms:
3.833333334 + x = 3.919325339

Solving
3.833333334 + x = 3.919325339

Solving for variable 'x'.

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

Add '-3.833333334' to each side of the equation.
3.833333334 + -3.833333334 + x = 3.919325339 + -3.833333334

Combine like terms: 3.833333334 + -3.833333334 = 0.000000000
0.000000000 + x = 3.919325339 + -3.833333334
x = 3.919325339 + -3.833333334

Combine like terms: 3.919325339 + -3.833333334 = 0.085992005
x = 0.085992005

Simplifying
x = 0.085992005


Subproblem 2
x + 3.833333334 = -3.919325339

Simplifying
x + 3.833333334 = -3.919325339

Reorder the terms:
3.833333334 + x = -3.919325339

Solving
3.833333334 + x = -3.919325339

Solving for variable 'x'.

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

Add '-3.833333334' to each side of the equation.
3.833333334 + -3.833333334 + x = -3.919325339 + -3.833333334

Combine like terms: 3.833333334 + -3.833333334 = 0.000000000
0.000000000 + x = -3.919325339 + -3.833333334
x = -3.919325339 + -3.833333334

Combine like terms: -3.919325339 + -3.833333334 = -7.752658673
x = -7.752658673

Simplifying
x = -7.752658673


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.085992005, -7.752658673}

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