3x^2+2x-45=0

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


Simplifying
3x2 + 2x + -45 = 0

Reorder the terms:
-45 + 2x + 3x2 = 0

Solving
-45 + 2x + 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 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 0.6666666667x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + 0.6666666667x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 0.6666666667x + x2 = 0 + 15
0.6666666667x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
0.6666666667x + x2 = 15

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 15 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 15 + 0.1111111112

Combine like terms: 15 + 0.1111111112 = 15.1111111112
0.1111111112 + 0.6666666667x + x2 = 15.1111111112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 15.1111111112

Calculate the square root of the right side: 3.887301263

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 3.887301263 and -3.887301263.


Subproblem 1
x + 0.3333333334 = 3.887301263

Simplifying
x + 0.3333333334 = 3.887301263

Reorder the terms:
0.3333333334 + x = 3.887301263

Solving
0.3333333334 + x = 3.887301263

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 3.887301263 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 3.887301263 + -0.3333333334
x = 3.887301263 + -0.3333333334

Combine like terms: 3.887301263 + -0.3333333334 = 3.5539679296
x = 3.5539679296

Simplifying
x = 3.5539679296


Subproblem 2
x + 0.3333333334 = -3.887301263

Simplifying
x + 0.3333333334 = -3.887301263

Reorder the terms:
0.3333333334 + x = -3.887301263

Solving
0.3333333334 + x = -3.887301263

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -3.887301263 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -3.887301263 + -0.3333333334
x = -3.887301263 + -0.3333333334

Combine like terms: -3.887301263 + -0.3333333334 = -4.2206345964
x = -4.2206345964

Simplifying
x = -4.2206345964


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.5539679296, -4.2206345964}

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