3x^2+242x+45=0

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Solution for 3x^2+242x+45=0 equation: 


Simplifying
3x2 + 242x + 45 = 0

Reorder the terms:
45 + 242x + 3x2 = 0

Solving
45 + 242x + 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'.
15 + 80.66666667x + x2 = 0

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 80.66666667x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + 80.66666667x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 80.66666667x + x2 = 0 + -15
80.66666667x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
80.66666667x + x2 = -15

The x term is 80.66666667x.  Take half its coefficient (40.33333334).
Square it (1626.777778) and add it to both sides.

Add '1626.777778' to each side of the equation.
80.66666667x + 1626.777778 + x2 = -15 + 1626.777778

Reorder the terms:
1626.777778 + 80.66666667x + x2 = -15 + 1626.777778

Combine like terms: -15 + 1626.777778 = 1611.777778
1626.777778 + 80.66666667x + x2 = 1611.777778

Factor a perfect square on the left side:
(x + 40.33333334)(x + 40.33333334) = 1611.777778

Calculate the square root of the right side: 40.146952288

Break this problem into two subproblems by setting 
(x + 40.33333334) equal to 40.146952288 and -40.146952288.


Subproblem 1
x + 40.33333334 = 40.146952288

Simplifying
x + 40.33333334 = 40.146952288

Reorder the terms:
40.33333334 + x = 40.146952288

Solving
40.33333334 + x = 40.146952288

Solving for variable 'x'.

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

Add '-40.33333334' to each side of the equation.
40.33333334 + -40.33333334 + x = 40.146952288 + -40.33333334

Combine like terms: 40.33333334 + -40.33333334 = 0.00000000
0.00000000 + x = 40.146952288 + -40.33333334
x = 40.146952288 + -40.33333334

Combine like terms: 40.146952288 + -40.33333334 = -0.186381052
x = -0.186381052

Simplifying
x = -0.186381052


Subproblem 2
x + 40.33333334 = -40.146952288

Simplifying
x + 40.33333334 = -40.146952288

Reorder the terms:
40.33333334 + x = -40.146952288

Solving
40.33333334 + x = -40.146952288

Solving for variable 'x'.

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

Add '-40.33333334' to each side of the equation.
40.33333334 + -40.33333334 + x = -40.146952288 + -40.33333334

Combine like terms: 40.33333334 + -40.33333334 = 0.00000000
0.00000000 + x = -40.146952288 + -40.33333334
x = -40.146952288 + -40.33333334

Combine like terms: -40.146952288 + -40.33333334 = -80.480285628
x = -80.480285628

Simplifying
x = -80.480285628


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.186381052, -80.480285628}

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