6x^2+17x-40=0

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Solution for 6x^2+17x-40=0 equation: 


Simplifying
6x2 + 17x + -40 = 0

Reorder the terms:
-40 + 17x + 6x2 = 0

Solving
-40 + 17x + 6x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
-6.666666667 + 2.833333333x + x2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + 2.833333333x + 6.666666667 + x2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + 2.833333333x + x2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + 2.833333333x + x2 = 0 + 6.666666667
2.833333333x + x2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
2.833333333x + x2 = 6.666666667

The x term is 2.833333333x.  Take half its coefficient (1.416666667).
Square it (2.006944445) and add it to both sides.

Add '2.006944445' to each side of the equation.
2.833333333x + 2.006944445 + x2 = 6.666666667 + 2.006944445

Reorder the terms:
2.006944445 + 2.833333333x + x2 = 6.666666667 + 2.006944445

Combine like terms: 6.666666667 + 2.006944445 = 8.673611112
2.006944445 + 2.833333333x + x2 = 8.673611112

Factor a perfect square on the left side:
(x + 1.416666667)(x + 1.416666667) = 8.673611112

Calculate the square root of the right side: 2.945099508

Break this problem into two subproblems by setting 
(x + 1.416666667) equal to 2.945099508 and -2.945099508.


Subproblem 1
x + 1.416666667 = 2.945099508

Simplifying
x + 1.416666667 = 2.945099508

Reorder the terms:
1.416666667 + x = 2.945099508

Solving
1.416666667 + x = 2.945099508

Solving for variable 'x'.

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

Add '-1.416666667' to each side of the equation.
1.416666667 + -1.416666667 + x = 2.945099508 + -1.416666667

Combine like terms: 1.416666667 + -1.416666667 = 0.000000000
0.000000000 + x = 2.945099508 + -1.416666667
x = 2.945099508 + -1.416666667

Combine like terms: 2.945099508 + -1.416666667 = 1.528432841
x = 1.528432841

Simplifying
x = 1.528432841


Subproblem 2
x + 1.416666667 = -2.945099508

Simplifying
x + 1.416666667 = -2.945099508

Reorder the terms:
1.416666667 + x = -2.945099508

Solving
1.416666667 + x = -2.945099508

Solving for variable 'x'.

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

Add '-1.416666667' to each side of the equation.
1.416666667 + -1.416666667 + x = -2.945099508 + -1.416666667

Combine like terms: 1.416666667 + -1.416666667 = 0.000000000
0.000000000 + x = -2.945099508 + -1.416666667
x = -2.945099508 + -1.416666667

Combine like terms: -2.945099508 + -1.416666667 = -4.361766175
x = -4.361766175

Simplifying
x = -4.361766175


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.528432841, -4.361766175}

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