3x^2+14x-240=0

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Solution for 3x^2+14x-240=0 equation: 


Simplifying
3x2 + 14x + -240 = 0

Reorder the terms:
-240 + 14x + 3x2 = 0

Solving
-240 + 14x + 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'.
-80 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + 4.666666667x + 80 + x2 = 0 + 80

Reorder the terms:
-80 + 80 + 4.666666667x + x2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + 4.666666667x + x2 = 0 + 80
4.666666667x + x2 = 0 + 80

Combine like terms: 0 + 80 = 80
4.666666667x + x2 = 80

The x term is 4.666666667x.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667x + 5.444444448 + x2 = 80 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = 80 + 5.444444448

Combine like terms: 80 + 5.444444448 = 85.444444448
5.444444448 + 4.666666667x + x2 = 85.444444448

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 85.444444448

Calculate the square root of the right side: 9.243616416

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 9.243616416 and -9.243616416.


Subproblem 1
x + 2.333333334 = 9.243616416

Simplifying
x + 2.333333334 = 9.243616416

Reorder the terms:
2.333333334 + x = 9.243616416

Solving
2.333333334 + x = 9.243616416

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = 9.243616416 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = 9.243616416 + -2.333333334
x = 9.243616416 + -2.333333334

Combine like terms: 9.243616416 + -2.333333334 = 6.910283082
x = 6.910283082

Simplifying
x = 6.910283082


Subproblem 2
x + 2.333333334 = -9.243616416

Simplifying
x + 2.333333334 = -9.243616416

Reorder the terms:
2.333333334 + x = -9.243616416

Solving
2.333333334 + x = -9.243616416

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = -9.243616416 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = -9.243616416 + -2.333333334
x = -9.243616416 + -2.333333334

Combine like terms: -9.243616416 + -2.333333334 = -11.57694975
x = -11.57694975

Simplifying
x = -11.57694975


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.910283082, -11.57694975}

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