3x^2-17x-40=0

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Solution for 3x^2-17x-40=0 equation: 


Simplifying
3x2 + -17x + -40 = 0

Reorder the terms:
-40 + -17x + 3x2 = 0

Solving
-40 + -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'.
-13.33333333 + -5.666666667x + x2 = 0

Move the constant term to the right:

Add '13.33333333' to each side of the equation.
-13.33333333 + -5.666666667x + 13.33333333 + x2 = 0 + 13.33333333

Reorder the terms:
-13.33333333 + 13.33333333 + -5.666666667x + x2 = 0 + 13.33333333

Combine like terms: -13.33333333 + 13.33333333 = 0.00000000
0.00000000 + -5.666666667x + x2 = 0 + 13.33333333
-5.666666667x + x2 = 0 + 13.33333333

Combine like terms: 0 + 13.33333333 = 13.33333333
-5.666666667x + x2 = 13.33333333

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 = 13.33333333 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667x + x2 = 13.33333333 + 8.027777782

Combine like terms: 13.33333333 + 8.027777782 = 21.361111112
8.027777782 + -5.666666667x + x2 = 21.361111112

Factor a perfect square on the left side:
(x + -2.833333334)(x + -2.833333334) = 21.361111112

Calculate the square root of the right side: 4.621808208

Break this problem into two subproblems by setting 
(x + -2.833333334) equal to 4.621808208 and -4.621808208.


Subproblem 1
x + -2.833333334 = 4.621808208

Simplifying
x + -2.833333334 = 4.621808208

Reorder the terms:
-2.833333334 + x = 4.621808208

Solving
-2.833333334 + x = 4.621808208

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 = 4.621808208 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = 4.621808208 + 2.833333334
x = 4.621808208 + 2.833333334

Combine like terms: 4.621808208 + 2.833333334 = 7.455141542
x = 7.455141542

Simplifying
x = 7.455141542


Subproblem 2
x + -2.833333334 = -4.621808208

Simplifying
x + -2.833333334 = -4.621808208

Reorder the terms:
-2.833333334 + x = -4.621808208

Solving
-2.833333334 + x = -4.621808208

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 = -4.621808208 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = -4.621808208 + 2.833333334
x = -4.621808208 + 2.833333334

Combine like terms: -4.621808208 + 2.833333334 = -1.788474874
x = -1.788474874

Simplifying
x = -1.788474874


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.455141542, -1.788474874}

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