3x^2+10x-36=0

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Solution for 3x^2+10x-36=0 equation: 


Simplifying
3x2 + 10x + -36 = 0

Reorder the terms:
-36 + 10x + 3x2 = 0

Solving
-36 + 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'.
-12 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 3.333333333x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 3.333333333x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 3.333333333x + x2 = 0 + 12
3.333333333x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
3.333333333x + x2 = 12

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 = 12 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = 12 + 2.777777779

Combine like terms: 12 + 2.777777779 = 14.777777779
2.777777779 + 3.333333333x + x2 = 14.777777779

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 14.777777779

Calculate the square root of the right side: 3.844187532

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 3.844187532 and -3.844187532.


Subproblem 1
x + 1.666666667 = 3.844187532

Simplifying
x + 1.666666667 = 3.844187532

Reorder the terms:
1.666666667 + x = 3.844187532

Solving
1.666666667 + x = 3.844187532

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 = 3.844187532 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = 3.844187532 + -1.666666667
x = 3.844187532 + -1.666666667

Combine like terms: 3.844187532 + -1.666666667 = 2.177520865
x = 2.177520865

Simplifying
x = 2.177520865


Subproblem 2
x + 1.666666667 = -3.844187532

Simplifying
x + 1.666666667 = -3.844187532

Reorder the terms:
1.666666667 + x = -3.844187532

Solving
1.666666667 + x = -3.844187532

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 = -3.844187532 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = -3.844187532 + -1.666666667
x = -3.844187532 + -1.666666667

Combine like terms: -3.844187532 + -1.666666667 = -5.510854199
x = -5.510854199

Simplifying
x = -5.510854199


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.177520865, -5.510854199}

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