3x^2+20x+21=0

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Solution for 3x^2+20x+21=0 equation: 


Simplifying
3x2 + 20x + 21 = 0

Reorder the terms:
21 + 20x + 3x2 = 0

Solving
21 + 20x + 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'.
7 + 6.666666667x + x2 = 0

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 6.666666667x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 6.666666667x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 6.666666667x + x2 = 0 + -7
6.666666667x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
6.666666667x + x2 = -7

The x term is 6.666666667x.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667x + 11.11111112 + x2 = -7 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667x + x2 = -7 + 11.11111112

Combine like terms: -7 + 11.11111112 = 4.11111112
11.11111112 + 6.666666667x + x2 = 4.11111112

Factor a perfect square on the left side:
(x + 3.333333334)(x + 3.333333334) = 4.11111112

Calculate the square root of the right side: 2.027587512

Break this problem into two subproblems by setting 
(x + 3.333333334) equal to 2.027587512 and -2.027587512.


Subproblem 1
x + 3.333333334 = 2.027587512

Simplifying
x + 3.333333334 = 2.027587512

Reorder the terms:
3.333333334 + x = 2.027587512

Solving
3.333333334 + x = 2.027587512

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = 2.027587512 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = 2.027587512 + -3.333333334
x = 2.027587512 + -3.333333334

Combine like terms: 2.027587512 + -3.333333334 = -1.305745822
x = -1.305745822

Simplifying
x = -1.305745822


Subproblem 2
x + 3.333333334 = -2.027587512

Simplifying
x + 3.333333334 = -2.027587512

Reorder the terms:
3.333333334 + x = -2.027587512

Solving
3.333333334 + x = -2.027587512

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = -2.027587512 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = -2.027587512 + -3.333333334
x = -2.027587512 + -3.333333334

Combine like terms: -2.027587512 + -3.333333334 = -5.360920846
x = -5.360920846

Simplifying
x = -5.360920846


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.305745822, -5.360920846}

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