9x^2+x-40=0

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Solution for 9x^2+x-40=0 equation: 


Simplifying
9x2 + x + -40 = 0

Reorder the terms:
-40 + x + 9x2 = 0

Solving
-40 + x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-4.444444444 + 0.1111111111x + x2 = 0

Move the constant term to the right:

Add '4.444444444' to each side of the equation.
-4.444444444 + 0.1111111111x + 4.444444444 + x2 = 0 + 4.444444444

Reorder the terms:
-4.444444444 + 4.444444444 + 0.1111111111x + x2 = 0 + 4.444444444

Combine like terms: -4.444444444 + 4.444444444 = 0.000000000
0.000000000 + 0.1111111111x + x2 = 0 + 4.444444444
0.1111111111x + x2 = 0 + 4.444444444

Combine like terms: 0 + 4.444444444 = 4.444444444
0.1111111111x + x2 = 4.444444444

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.1111111111x + 0.25 + x2 = 4.444444444 + 0.25

Reorder the terms:
0.25 + 0.1111111111x + x2 = 4.444444444 + 0.25

Combine like terms: 4.444444444 + 0.25 = 4.694444444
0.25 + 0.1111111111x + x2 = 4.694444444

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 4.694444444

Calculate the square root of the right side: 2.166666667

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.166666667 and -2.166666667.


Subproblem 1
x + 0.5 = 2.166666667

Simplifying
x + 0.5 = 2.166666667

Reorder the terms:
0.5 + x = 2.166666667

Solving
0.5 + x = 2.166666667

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 2.166666667 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.166666667 + -0.5
x = 2.166666667 + -0.5

Combine like terms: 2.166666667 + -0.5 = 1.666666667
x = 1.666666667

Simplifying
x = 1.666666667


Subproblem 2
x + 0.5 = -2.166666667

Simplifying
x + 0.5 = -2.166666667

Reorder the terms:
0.5 + x = -2.166666667

Solving
0.5 + x = -2.166666667

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -2.166666667 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.166666667 + -0.5
x = -2.166666667 + -0.5

Combine like terms: -2.166666667 + -0.5 = -2.666666667
x = -2.666666667

Simplifying
x = -2.666666667


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.666666667, -2.666666667}

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