6x^2+17x-50=0

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Solution for 6x^2+17x-50=0 equation: 


Simplifying
6x2 + 17x + -50 = 0

Reorder the terms:
-50 + 17x + 6x2 = 0

Solving
-50 + 17x + 6x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
-8.333333333 + 2.833333333x + x2 = 0

Move the constant term to the right:

Add '8.333333333' to each side of the equation.
-8.333333333 + 2.833333333x + 8.333333333 + x2 = 0 + 8.333333333

Reorder the terms:
-8.333333333 + 8.333333333 + 2.833333333x + x2 = 0 + 8.333333333

Combine like terms: -8.333333333 + 8.333333333 = 0.000000000
0.000000000 + 2.833333333x + x2 = 0 + 8.333333333
2.833333333x + x2 = 0 + 8.333333333

Combine like terms: 0 + 8.333333333 = 8.333333333
2.833333333x + x2 = 8.333333333

The x term is 2.833333333x.  Take half its coefficient (1.416666667).
Square it (2.006944445) and add it to both sides.

Add '2.006944445' to each side of the equation.
2.833333333x + 2.006944445 + x2 = 8.333333333 + 2.006944445

Reorder the terms:
2.006944445 + 2.833333333x + x2 = 8.333333333 + 2.006944445

Combine like terms: 8.333333333 + 2.006944445 = 10.340277778
2.006944445 + 2.833333333x + x2 = 10.340277778

Factor a perfect square on the left side:
(x + 1.416666667)(x + 1.416666667) = 10.340277778

Calculate the square root of the right side: 3.21563023

Break this problem into two subproblems by setting 
(x + 1.416666667) equal to 3.21563023 and -3.21563023.


Subproblem 1
x + 1.416666667 = 3.21563023

Simplifying
x + 1.416666667 = 3.21563023

Reorder the terms:
1.416666667 + x = 3.21563023

Solving
1.416666667 + x = 3.21563023

Solving for variable 'x'.

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

Add '-1.416666667' to each side of the equation.
1.416666667 + -1.416666667 + x = 3.21563023 + -1.416666667

Combine like terms: 1.416666667 + -1.416666667 = 0.000000000
0.000000000 + x = 3.21563023 + -1.416666667
x = 3.21563023 + -1.416666667

Combine like terms: 3.21563023 + -1.416666667 = 1.798963563
x = 1.798963563

Simplifying
x = 1.798963563


Subproblem 2
x + 1.416666667 = -3.21563023

Simplifying
x + 1.416666667 = -3.21563023

Reorder the terms:
1.416666667 + x = -3.21563023

Solving
1.416666667 + x = -3.21563023

Solving for variable 'x'.

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

Add '-1.416666667' to each side of the equation.
1.416666667 + -1.416666667 + x = -3.21563023 + -1.416666667

Combine like terms: 1.416666667 + -1.416666667 = 0.000000000
0.000000000 + x = -3.21563023 + -1.416666667
x = -3.21563023 + -1.416666667

Combine like terms: -3.21563023 + -1.416666667 = -4.632296897
x = -4.632296897

Simplifying
x = -4.632296897


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.798963563, -4.632296897}

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