3x^2+21x-8=0

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Solution for 3x^2+21x-8=0 equation: 


Simplifying
3x2 + 21x + -8 = 0

Reorder the terms:
-8 + 21x + 3x2 = 0

Solving
-8 + 21x + 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'.
-2.666666667 + 7x + x2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + 7x + 2.666666667 + x2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + 7x + x2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + 7x + x2 = 0 + 2.666666667
7x + x2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
7x + x2 = 2.666666667

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 2.666666667 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 2.666666667 + 12.25

Combine like terms: 2.666666667 + 12.25 = 14.916666667
12.25 + 7x + x2 = 14.916666667

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 14.916666667

Calculate the square root of the right side: 3.862210075

Break this problem into two subproblems by setting 
(x + 3.5) equal to 3.862210075 and -3.862210075.


Subproblem 1
x + 3.5 = 3.862210075

Simplifying
x + 3.5 = 3.862210075

Reorder the terms:
3.5 + x = 3.862210075

Solving
3.5 + x = 3.862210075

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 3.862210075 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 3.862210075 + -3.5
x = 3.862210075 + -3.5

Combine like terms: 3.862210075 + -3.5 = 0.362210075
x = 0.362210075

Simplifying
x = 0.362210075


Subproblem 2
x + 3.5 = -3.862210075

Simplifying
x + 3.5 = -3.862210075

Reorder the terms:
3.5 + x = -3.862210075

Solving
3.5 + x = -3.862210075

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -3.862210075 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -3.862210075 + -3.5
x = -3.862210075 + -3.5

Combine like terms: -3.862210075 + -3.5 = -7.362210075
x = -7.362210075

Simplifying
x = -7.362210075


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.362210075, -7.362210075}

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