3x^2+15x+8=0

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Solution for 3x^2+15x+8=0 equation: 


Simplifying
3x2 + 15x + 8 = 0

Reorder the terms:
8 + 15x + 3x2 = 0

Solving
8 + 15x + 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 + 5x + x2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + 5x + -2.666666667 + x2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + 5x + x2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + 5x + x2 = 0 + -2.666666667
5x + x2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
5x + x2 = -2.666666667

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -2.666666667 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -2.666666667 + 6.25

Combine like terms: -2.666666667 + 6.25 = 3.583333333
6.25 + 5x + x2 = 3.583333333

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 3.583333333

Calculate the square root of the right side: 1.892969449

Break this problem into two subproblems by setting 
(x + 2.5) equal to 1.892969449 and -1.892969449.


Subproblem 1
x + 2.5 = 1.892969449

Simplifying
x + 2.5 = 1.892969449

Reorder the terms:
2.5 + x = 1.892969449

Solving
2.5 + x = 1.892969449

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 1.892969449 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 1.892969449 + -2.5
x = 1.892969449 + -2.5

Combine like terms: 1.892969449 + -2.5 = -0.607030551
x = -0.607030551

Simplifying
x = -0.607030551


Subproblem 2
x + 2.5 = -1.892969449

Simplifying
x + 2.5 = -1.892969449

Reorder the terms:
2.5 + x = -1.892969449

Solving
2.5 + x = -1.892969449

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -1.892969449 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -1.892969449 + -2.5
x = -1.892969449 + -2.5

Combine like terms: -1.892969449 + -2.5 = -4.392969449
x = -4.392969449

Simplifying
x = -4.392969449


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.607030551, -4.392969449}

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