3x^2-18x-50=0

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Solution for 3x^2-18x-50=0 equation:


Simplifying
3x2 + -18x + -50 = 0

Reorder the terms:
-50 + -18x + 3x2 = 0

Solving
-50 + -18x + 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 + -6x + x2 = 0

Move the constant term to the right:

Add '16.66666667' to each side of the equation.
-16.66666667 + -6x + 16.66666667 + x2 = 0 + 16.66666667

Reorder the terms:
-16.66666667 + 16.66666667 + -6x + x2 = 0 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + -6x + x2 = 0 + 16.66666667
-6x + x2 = 0 + 16.66666667

Combine like terms: 0 + 16.66666667 = 16.66666667
-6x + x2 = 16.66666667

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 16.66666667 + 9

Reorder the terms:
9 + -6x + x2 = 16.66666667 + 9

Combine like terms: 16.66666667 + 9 = 25.66666667
9 + -6x + x2 = 25.66666667

Factor a perfect square on the left side:
(x + -3)(x + -3) = 25.66666667

Calculate the square root of the right side: 5.066228052

Break this problem into two subproblems by setting 
(x + -3) equal to 5.066228052 and -5.066228052.

Subproblem 1

x + -3 = 5.066228052 Simplifying x + -3 = 5.066228052 Reorder the terms: -3 + x = 5.066228052 Solving -3 + x = 5.066228052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 5.066228052 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.066228052 + 3 x = 5.066228052 + 3 Combine like terms: 5.066228052 + 3 = 8.066228052 x = 8.066228052 Simplifying x = 8.066228052

Subproblem 2

x + -3 = -5.066228052 Simplifying x + -3 = -5.066228052 Reorder the terms: -3 + x = -5.066228052 Solving -3 + x = -5.066228052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -5.066228052 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.066228052 + 3 x = -5.066228052 + 3 Combine like terms: -5.066228052 + 3 = -2.066228052 x = -2.066228052 Simplifying x = -2.066228052

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.066228052, -2.066228052}

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