21X^2+70X-50=0

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Solution for 21X^2+70X-50=0 equation: 


Simplifying
21X2 + 70X + -50 = 0

Reorder the terms:
-50 + 70X + 21X2 = 0

Solving
-50 + 70X + 21X2 = 0

Solving for variable 'X'.

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

Divide each side by '21'.
-2.380952381 + 3.333333333X + X2 = 0

Move the constant term to the right:

Add '2.380952381' to each side of the equation.
-2.380952381 + 3.333333333X + 2.380952381 + X2 = 0 + 2.380952381

Reorder the terms:
-2.380952381 + 2.380952381 + 3.333333333X + X2 = 0 + 2.380952381

Combine like terms: -2.380952381 + 2.380952381 = 0.000000000
0.000000000 + 3.333333333X + X2 = 0 + 2.380952381
3.333333333X + X2 = 0 + 2.380952381

Combine like terms: 0 + 2.380952381 = 2.380952381
3.333333333X + X2 = 2.380952381

The X term is 3.333333333X.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333X + 2.777777779 + X2 = 2.380952381 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333X + X2 = 2.380952381 + 2.777777779

Combine like terms: 2.380952381 + 2.777777779 = 5.15873016
2.777777779 + 3.333333333X + X2 = 5.15873016

Factor a perfect square on the left side:
(X + 1.666666667)(X + 1.666666667) = 5.15873016

Calculate the square root of the right side: 2.271283813

Break this problem into two subproblems by setting 
(X + 1.666666667) equal to 2.271283813 and -2.271283813.


Subproblem 1
X + 1.666666667 = 2.271283813

Simplifying
X + 1.666666667 = 2.271283813

Reorder the terms:
1.666666667 + X = 2.271283813

Solving
1.666666667 + X = 2.271283813

Solving for variable 'X'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + X = 2.271283813 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + X = 2.271283813 + -1.666666667
X = 2.271283813 + -1.666666667

Combine like terms: 2.271283813 + -1.666666667 = 0.604617146
X = 0.604617146

Simplifying
X = 0.604617146


Subproblem 2
X + 1.666666667 = -2.271283813

Simplifying
X + 1.666666667 = -2.271283813

Reorder the terms:
1.666666667 + X = -2.271283813

Solving
1.666666667 + X = -2.271283813

Solving for variable 'X'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + X = -2.271283813 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + X = -2.271283813 + -1.666666667
X = -2.271283813 + -1.666666667

Combine like terms: -2.271283813 + -1.666666667 = -3.93795048
X = -3.93795048

Simplifying
X = -3.93795048


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.604617146, -3.93795048}

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