3x^2+5x-95=0

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Solution for 3x^2+5x-95=0 equation: 


Simplifying
3x2 + 5x + -95 = 0

Reorder the terms:
-95 + 5x + 3x2 = 0

Solving
-95 + 5x + 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'.
-31.66666667 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '31.66666667' to each side of the equation.
-31.66666667 + 1.666666667x + 31.66666667 + x2 = 0 + 31.66666667

Reorder the terms:
-31.66666667 + 31.66666667 + 1.666666667x + x2 = 0 + 31.66666667

Combine like terms: -31.66666667 + 31.66666667 = 0.00000000
0.00000000 + 1.666666667x + x2 = 0 + 31.66666667
1.666666667x + x2 = 0 + 31.66666667

Combine like terms: 0 + 31.66666667 = 31.66666667
1.666666667x + x2 = 31.66666667

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 31.66666667 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 31.66666667 + 0.6944444447

Combine like terms: 31.66666667 + 0.6944444447 = 32.3611111147
0.6944444447 + 1.666666667x + x2 = 32.3611111147

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 32.3611111147

Calculate the square root of the right side: 5.688682722

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 5.688682722 and -5.688682722.


Subproblem 1
x + 0.8333333335 = 5.688682722

Simplifying
x + 0.8333333335 = 5.688682722

Reorder the terms:
0.8333333335 + x = 5.688682722

Solving
0.8333333335 + x = 5.688682722

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 5.688682722 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 5.688682722 + -0.8333333335
x = 5.688682722 + -0.8333333335

Combine like terms: 5.688682722 + -0.8333333335 = 4.8553493885
x = 4.8553493885

Simplifying
x = 4.8553493885


Subproblem 2
x + 0.8333333335 = -5.688682722

Simplifying
x + 0.8333333335 = -5.688682722

Reorder the terms:
0.8333333335 + x = -5.688682722

Solving
0.8333333335 + x = -5.688682722

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -5.688682722 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -5.688682722 + -0.8333333335
x = -5.688682722 + -0.8333333335

Combine like terms: -5.688682722 + -0.8333333335 = -6.5220160555
x = -6.5220160555

Simplifying
x = -6.5220160555


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.8553493885, -6.5220160555}

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