3x^2+17x+21=0

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Solution for 3x^2+17x+21=0 equation: 


Simplifying
3x2 + 17x + 21 = 0

Reorder the terms:
21 + 17x + 3x2 = 0

Solving
21 + 17x + 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 + 5.666666667x + x2 = 0

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 5.666666667x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 5.666666667x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5.666666667x + x2 = 0 + -7
5.666666667x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
5.666666667x + x2 = -7

The x term is 5.666666667x.  Take half its coefficient (2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
5.666666667x + 8.027777782 + x2 = -7 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667x + x2 = -7 + 8.027777782

Combine like terms: -7 + 8.027777782 = 1.027777782
8.027777782 + 5.666666667x + x2 = 1.027777782

Factor a perfect square on the left side:
(x + 2.833333334)(x + 2.833333334) = 1.027777782

Calculate the square root of the right side: 1.013793757

Break this problem into two subproblems by setting 
(x + 2.833333334) equal to 1.013793757 and -1.013793757.


Subproblem 1
x + 2.833333334 = 1.013793757

Simplifying
x + 2.833333334 = 1.013793757

Reorder the terms:
2.833333334 + x = 1.013793757

Solving
2.833333334 + x = 1.013793757

Solving for variable 'x'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + x = 1.013793757 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + x = 1.013793757 + -2.833333334
x = 1.013793757 + -2.833333334

Combine like terms: 1.013793757 + -2.833333334 = -1.819539577
x = -1.819539577

Simplifying
x = -1.819539577


Subproblem 2
x + 2.833333334 = -1.013793757

Simplifying
x + 2.833333334 = -1.013793757

Reorder the terms:
2.833333334 + x = -1.013793757

Solving
2.833333334 + x = -1.013793757

Solving for variable 'x'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + x = -1.013793757 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + x = -1.013793757 + -2.833333334
x = -1.013793757 + -2.833333334

Combine like terms: -1.013793757 + -2.833333334 = -3.847127091
x = -3.847127091

Simplifying
x = -3.847127091


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.819539577, -3.847127091}

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