3x^2+21x-6.7=0

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Solution for 3x^2+21x-6.7=0 equation: 


Simplifying
3x2 + 21x + -6.7 = 0

Reorder the terms:
-6.7 + 21x + 3x2 = 0

Solving
-6.7 + 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'.
-2.233333333 + 7x + x2 = 0

Move the constant term to the right:

Add '2.233333333' to each side of the equation.
-2.233333333 + 7x + 2.233333333 + x2 = 0 + 2.233333333

Reorder the terms:
-2.233333333 + 2.233333333 + 7x + x2 = 0 + 2.233333333

Combine like terms: -2.233333333 + 2.233333333 = 0.000000000
0.000000000 + 7x + x2 = 0 + 2.233333333
7x + x2 = 0 + 2.233333333

Combine like terms: 0 + 2.233333333 = 2.233333333
7x + x2 = 2.233333333

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 = 2.233333333 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 2.233333333 + 12.25

Combine like terms: 2.233333333 + 12.25 = 14.483333333
12.25 + 7x + x2 = 14.483333333

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 14.483333333

Calculate the square root of the right side: 3.805697483

Break this problem into two subproblems by setting 
(x + 3.5) equal to 3.805697483 and -3.805697483.


Subproblem 1
x + 3.5 = 3.805697483

Simplifying
x + 3.5 = 3.805697483

Reorder the terms:
3.5 + x = 3.805697483

Solving
3.5 + x = 3.805697483

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 = 3.805697483 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 3.805697483 + -3.5
x = 3.805697483 + -3.5

Combine like terms: 3.805697483 + -3.5 = 0.305697483
x = 0.305697483

Simplifying
x = 0.305697483


Subproblem 2
x + 3.5 = -3.805697483

Simplifying
x + 3.5 = -3.805697483

Reorder the terms:
3.5 + x = -3.805697483

Solving
3.5 + x = -3.805697483

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 = -3.805697483 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -3.805697483 + -3.5
x = -3.805697483 + -3.5

Combine like terms: -3.805697483 + -3.5 = -7.305697483
x = -7.305697483

Simplifying
x = -7.305697483


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.305697483, -7.305697483}

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