3x^2+10x-1160=0

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Solution for 3x^2+10x-1160=0 equation: 


Simplifying
3x2 + 10x + -1160 = 0

Reorder the terms:
-1160 + 10x + 3x2 = 0

Solving
-1160 + 10x + 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'.
-386.6666667 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '386.6666667' to each side of the equation.
-386.6666667 + 3.333333333x + 386.6666667 + x2 = 0 + 386.6666667

Reorder the terms:
-386.6666667 + 386.6666667 + 3.333333333x + x2 = 0 + 386.6666667

Combine like terms: -386.6666667 + 386.6666667 = 0.0000000
0.0000000 + 3.333333333x + x2 = 0 + 386.6666667
3.333333333x + x2 = 0 + 386.6666667

Combine like terms: 0 + 386.6666667 = 386.6666667
3.333333333x + x2 = 386.6666667

The x term is 3.333333333x.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333x + 2.777777779 + x2 = 386.6666667 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = 386.6666667 + 2.777777779

Combine like terms: 386.6666667 + 2.777777779 = 389.444444479
2.777777779 + 3.333333333x + x2 = 389.444444479

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 389.444444479

Calculate the square root of the right side: 19.734346822

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 19.734346822 and -19.734346822.


Subproblem 1
x + 1.666666667 = 19.734346822

Simplifying
x + 1.666666667 = 19.734346822

Reorder the terms:
1.666666667 + x = 19.734346822

Solving
1.666666667 + x = 19.734346822

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = 19.734346822 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = 19.734346822 + -1.666666667
x = 19.734346822 + -1.666666667

Combine like terms: 19.734346822 + -1.666666667 = 18.067680155
x = 18.067680155

Simplifying
x = 18.067680155


Subproblem 2
x + 1.666666667 = -19.734346822

Simplifying
x + 1.666666667 = -19.734346822

Reorder the terms:
1.666666667 + x = -19.734346822

Solving
1.666666667 + x = -19.734346822

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = -19.734346822 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = -19.734346822 + -1.666666667
x = -19.734346822 + -1.666666667

Combine like terms: -19.734346822 + -1.666666667 = -21.401013489
x = -21.401013489

Simplifying
x = -21.401013489


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.067680155, -21.401013489}

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