3x^2-25x-19=0

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Solution for 3x^2-25x-19=0 equation: 


Simplifying
3x2 + -25x + -19 = 0

Reorder the terms:
-19 + -25x + 3x2 = 0

Solving
-19 + -25x + 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'.
-6.333333333 + -8.333333333x + x2 = 0

Move the constant term to the right:

Add '6.333333333' to each side of the equation.
-6.333333333 + -8.333333333x + 6.333333333 + x2 = 0 + 6.333333333

Reorder the terms:
-6.333333333 + 6.333333333 + -8.333333333x + x2 = 0 + 6.333333333

Combine like terms: -6.333333333 + 6.333333333 = 0.000000000
0.000000000 + -8.333333333x + x2 = 0 + 6.333333333
-8.333333333x + x2 = 0 + 6.333333333

Combine like terms: 0 + 6.333333333 = 6.333333333
-8.333333333x + x2 = 6.333333333

The x term is -8.333333333x.  Take half its coefficient (-4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
-8.333333333x + 17.36111111 + x2 = 6.333333333 + 17.36111111

Reorder the terms:
17.36111111 + -8.333333333x + x2 = 6.333333333 + 17.36111111

Combine like terms: 6.333333333 + 17.36111111 = 23.694444443
17.36111111 + -8.333333333x + x2 = 23.694444443

Factor a perfect square on the left side:
(x + -4.166666667)(x + -4.166666667) = 23.694444443

Calculate the square root of the right side: 4.867693955

Break this problem into two subproblems by setting 
(x + -4.166666667) equal to 4.867693955 and -4.867693955.


Subproblem 1
x + -4.166666667 = 4.867693955

Simplifying
x + -4.166666667 = 4.867693955

Reorder the terms:
-4.166666667 + x = 4.867693955

Solving
-4.166666667 + x = 4.867693955

Solving for variable 'x'.

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

Add '4.166666667' to each side of the equation.
-4.166666667 + 4.166666667 + x = 4.867693955 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + x = 4.867693955 + 4.166666667
x = 4.867693955 + 4.166666667

Combine like terms: 4.867693955 + 4.166666667 = 9.034360622
x = 9.034360622

Simplifying
x = 9.034360622


Subproblem 2
x + -4.166666667 = -4.867693955

Simplifying
x + -4.166666667 = -4.867693955

Reorder the terms:
-4.166666667 + x = -4.867693955

Solving
-4.166666667 + x = -4.867693955

Solving for variable 'x'.

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

Add '4.166666667' to each side of the equation.
-4.166666667 + 4.166666667 + x = -4.867693955 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + x = -4.867693955 + 4.166666667
x = -4.867693955 + 4.166666667

Combine like terms: -4.867693955 + 4.166666667 = -0.701027288
x = -0.701027288

Simplifying
x = -0.701027288


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.034360622, -0.701027288}

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