3x^2+23x-3=0

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


Simplifying
3x2 + 23x + -3 = 0

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

Solving
-3 + 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'.
-1 + 7.666666667x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 7.666666667x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 7.666666667x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 7.666666667x + x2 = 0 + 1
7.666666667x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
7.666666667x + x2 = 1

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 = 1 + 14.69444445

Reorder the terms:
14.69444445 + 7.666666667x + x2 = 1 + 14.69444445

Combine like terms: 1 + 14.69444445 = 15.69444445
14.69444445 + 7.666666667x + x2 = 15.69444445

Factor a perfect square on the left side:
(x + 3.833333334)(x + 3.833333334) = 15.69444445

Calculate the square root of the right side: 3.961621442

Break this problem into two subproblems by setting 
(x + 3.833333334) equal to 3.961621442 and -3.961621442.


Subproblem 1
x + 3.833333334 = 3.961621442

Simplifying
x + 3.833333334 = 3.961621442

Reorder the terms:
3.833333334 + x = 3.961621442

Solving
3.833333334 + x = 3.961621442

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 = 3.961621442 + -3.833333334

Combine like terms: 3.833333334 + -3.833333334 = 0.000000000
0.000000000 + x = 3.961621442 + -3.833333334
x = 3.961621442 + -3.833333334

Combine like terms: 3.961621442 + -3.833333334 = 0.128288108
x = 0.128288108

Simplifying
x = 0.128288108


Subproblem 2
x + 3.833333334 = -3.961621442

Simplifying
x + 3.833333334 = -3.961621442

Reorder the terms:
3.833333334 + x = -3.961621442

Solving
3.833333334 + x = -3.961621442

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 = -3.961621442 + -3.833333334

Combine like terms: 3.833333334 + -3.833333334 = 0.000000000
0.000000000 + x = -3.961621442 + -3.833333334
x = -3.961621442 + -3.833333334

Combine like terms: -3.961621442 + -3.833333334 = -7.794954776
x = -7.794954776

Simplifying
x = -7.794954776


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.128288108, -7.794954776}

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