3x^2-17x-36=0

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Solution for 3x^2-17x-36=0 equation: 


Simplifying
3x2 + -17x + -36 = 0

Reorder the terms:
-36 + -17x + 3x2 = 0

Solving
-36 + -17x + 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 + -5.666666667x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -5.666666667x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -5.666666667x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -5.666666667x + x2 = 0 + 12
-5.666666667x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-5.666666667x + x2 = 12

The x term is -5.666666667x.  Take half its coefficient (-2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
-5.666666667x + 8.027777782 + x2 = 12 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667x + x2 = 12 + 8.027777782

Combine like terms: 12 + 8.027777782 = 20.027777782
8.027777782 + -5.666666667x + x2 = 20.027777782

Factor a perfect square on the left side:
(x + -2.833333334)(x + -2.833333334) = 20.027777782

Calculate the square root of the right side: 4.475240528

Break this problem into two subproblems by setting 
(x + -2.833333334) equal to 4.475240528 and -4.475240528.


Subproblem 1
x + -2.833333334 = 4.475240528

Simplifying
x + -2.833333334 = 4.475240528

Reorder the terms:
-2.833333334 + x = 4.475240528

Solving
-2.833333334 + x = 4.475240528

Solving for variable 'x'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + x = 4.475240528 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = 4.475240528 + 2.833333334
x = 4.475240528 + 2.833333334

Combine like terms: 4.475240528 + 2.833333334 = 7.308573862
x = 7.308573862

Simplifying
x = 7.308573862


Subproblem 2
x + -2.833333334 = -4.475240528

Simplifying
x + -2.833333334 = -4.475240528

Reorder the terms:
-2.833333334 + x = -4.475240528

Solving
-2.833333334 + x = -4.475240528

Solving for variable 'x'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + x = -4.475240528 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = -4.475240528 + 2.833333334
x = -4.475240528 + 2.833333334

Combine like terms: -4.475240528 + 2.833333334 = -1.641907194
x = -1.641907194

Simplifying
x = -1.641907194


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.308573862, -1.641907194}

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