3x^2+30x+25*3x+5=0

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Solution for 3x^2+30x+25*3x+5=0 equation: 


Simplifying
3x2 + 30x + 25 * 3x + 5 = 0

Multiply 25 * 3
3x2 + 30x + 75x + 5 = 0

Reorder the terms:
5 + 30x + 75x + 3x2 = 0

Combine like terms: 30x + 75x = 105x
5 + 105x + 3x2 = 0

Solving
5 + 105x + 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'.
1.666666667 + 35x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + 35x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + 35x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + 35x + x2 = 0 + -1.666666667
35x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
35x + x2 = -1.666666667

The x term is 35x.  Take half its coefficient (17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
35x + 306.25 + x2 = -1.666666667 + 306.25

Reorder the terms:
306.25 + 35x + x2 = -1.666666667 + 306.25

Combine like terms: -1.666666667 + 306.25 = 304.583333333
306.25 + 35x + x2 = 304.583333333

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 304.583333333

Calculate the square root of the right side: 17.452315988

Break this problem into two subproblems by setting 
(x + 17.5) equal to 17.452315988 and -17.452315988.


Subproblem 1
x + 17.5 = 17.452315988

Simplifying
x + 17.5 = 17.452315988

Reorder the terms:
17.5 + x = 17.452315988

Solving
17.5 + x = 17.452315988

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = 17.452315988 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = 17.452315988 + -17.5
x = 17.452315988 + -17.5

Combine like terms: 17.452315988 + -17.5 = -0.047684012
x = -0.047684012

Simplifying
x = -0.047684012


Subproblem 2
x + 17.5 = -17.452315988

Simplifying
x + 17.5 = -17.452315988

Reorder the terms:
17.5 + x = -17.452315988

Solving
17.5 + x = -17.452315988

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = -17.452315988 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = -17.452315988 + -17.5
x = -17.452315988 + -17.5

Combine like terms: -17.452315988 + -17.5 = -34.952315988
x = -34.952315988

Simplifying
x = -34.952315988


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.047684012, -34.952315988}

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