3x^2+103x+392.25=0

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Solution for 3x^2+103x+392.25=0 equation: 


Simplifying
3x2 + 103x + 392.25 = 0

Reorder the terms:
392.25 + 103x + 3x2 = 0

Solving
392.25 + 103x + 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'.
130.75 + 34.33333333x + x2 = 0

Move the constant term to the right:

Add '-130.75' to each side of the equation.
130.75 + 34.33333333x + -130.75 + x2 = 0 + -130.75

Reorder the terms:
130.75 + -130.75 + 34.33333333x + x2 = 0 + -130.75

Combine like terms: 130.75 + -130.75 = 0.00
0.00 + 34.33333333x + x2 = 0 + -130.75
34.33333333x + x2 = 0 + -130.75

Combine like terms: 0 + -130.75 = -130.75
34.33333333x + x2 = -130.75

The x term is 34.33333333x.  Take half its coefficient (17.16666667).
Square it (294.6944446) and add it to both sides.

Add '294.6944446' to each side of the equation.
34.33333333x + 294.6944446 + x2 = -130.75 + 294.6944446

Reorder the terms:
294.6944446 + 34.33333333x + x2 = -130.75 + 294.6944446

Combine like terms: -130.75 + 294.6944446 = 163.9444446
294.6944446 + 34.33333333x + x2 = 163.9444446

Factor a perfect square on the left side:
(x + 17.16666667)(x + 17.16666667) = 163.9444446

Calculate the square root of the right side: 12.804079217

Break this problem into two subproblems by setting 
(x + 17.16666667) equal to 12.804079217 and -12.804079217.


Subproblem 1
x + 17.16666667 = 12.804079217

Simplifying
x + 17.16666667 = 12.804079217

Reorder the terms:
17.16666667 + x = 12.804079217

Solving
17.16666667 + x = 12.804079217

Solving for variable 'x'.

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

Add '-17.16666667' to each side of the equation.
17.16666667 + -17.16666667 + x = 12.804079217 + -17.16666667

Combine like terms: 17.16666667 + -17.16666667 = 0.00000000
0.00000000 + x = 12.804079217 + -17.16666667
x = 12.804079217 + -17.16666667

Combine like terms: 12.804079217 + -17.16666667 = -4.362587453
x = -4.362587453

Simplifying
x = -4.362587453


Subproblem 2
x + 17.16666667 = -12.804079217

Simplifying
x + 17.16666667 = -12.804079217

Reorder the terms:
17.16666667 + x = -12.804079217

Solving
17.16666667 + x = -12.804079217

Solving for variable 'x'.

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

Add '-17.16666667' to each side of the equation.
17.16666667 + -17.16666667 + x = -12.804079217 + -17.16666667

Combine like terms: 17.16666667 + -17.16666667 = 0.00000000
0.00000000 + x = -12.804079217 + -17.16666667
x = -12.804079217 + -17.16666667

Combine like terms: -12.804079217 + -17.16666667 = -29.970745887
x = -29.970745887

Simplifying
x = -29.970745887


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-4.362587453, -29.970745887}

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