3x^2-15x-50=0

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Solution for 3x^2-15x-50=0 equation: 


Simplifying
3x2 + -15x + -50 = 0

Reorder the terms:
-50 + -15x + 3x2 = 0

Solving
-50 + -15x + 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'.
-16.66666667 + -5x + x2 = 0

Move the constant term to the right:

Add '16.66666667' to each side of the equation.
-16.66666667 + -5x + 16.66666667 + x2 = 0 + 16.66666667

Reorder the terms:
-16.66666667 + 16.66666667 + -5x + x2 = 0 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + -5x + x2 = 0 + 16.66666667
-5x + x2 = 0 + 16.66666667

Combine like terms: 0 + 16.66666667 = 16.66666667
-5x + x2 = 16.66666667

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 16.66666667 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 16.66666667 + 6.25

Combine like terms: 16.66666667 + 6.25 = 22.91666667
6.25 + -5x + x2 = 22.91666667

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 22.91666667

Calculate the square root of the right side: 4.787135539

Break this problem into two subproblems by setting 
(x + -2.5) equal to 4.787135539 and -4.787135539.


Subproblem 1
x + -2.5 = 4.787135539

Simplifying
x + -2.5 = 4.787135539

Reorder the terms:
-2.5 + x = 4.787135539

Solving
-2.5 + x = 4.787135539

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 4.787135539 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 4.787135539 + 2.5
x = 4.787135539 + 2.5

Combine like terms: 4.787135539 + 2.5 = 7.287135539
x = 7.287135539

Simplifying
x = 7.287135539


Subproblem 2
x + -2.5 = -4.787135539

Simplifying
x + -2.5 = -4.787135539

Reorder the terms:
-2.5 + x = -4.787135539

Solving
-2.5 + x = -4.787135539

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -4.787135539 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -4.787135539 + 2.5
x = -4.787135539 + 2.5

Combine like terms: -4.787135539 + 2.5 = -2.287135539
x = -2.287135539

Simplifying
x = -2.287135539


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.287135539, -2.287135539}

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