9x^2-40x-16=0

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Solution for 9x^2-40x-16=0 equation: 


Simplifying
9x2 + -40x + -16 = 0

Reorder the terms:
-16 + -40x + 9x2 = 0

Solving
-16 + -40x + 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'.
-1.777777778 + -4.444444444x + x2 = 0

Move the constant term to the right:

Add '1.777777778' to each side of the equation.
-1.777777778 + -4.444444444x + 1.777777778 + x2 = 0 + 1.777777778

Reorder the terms:
-1.777777778 + 1.777777778 + -4.444444444x + x2 = 0 + 1.777777778

Combine like terms: -1.777777778 + 1.777777778 = 0.000000000
0.000000000 + -4.444444444x + x2 = 0 + 1.777777778
-4.444444444x + x2 = 0 + 1.777777778

Combine like terms: 0 + 1.777777778 = 1.777777778
-4.444444444x + x2 = 1.777777778

The x term is -4.444444444x.  Take half its coefficient (-2.222222222).
Square it (4.938271604) and add it to both sides.

Add '4.938271604' to each side of the equation.
-4.444444444x + 4.938271604 + x2 = 1.777777778 + 4.938271604

Reorder the terms:
4.938271604 + -4.444444444x + x2 = 1.777777778 + 4.938271604

Combine like terms: 1.777777778 + 4.938271604 = 6.716049382
4.938271604 + -4.444444444x + x2 = 6.716049382

Factor a perfect square on the left side:
(x + -2.222222222)(x + -2.222222222) = 6.716049382

Calculate the square root of the right side: 2.591534175

Break this problem into two subproblems by setting 
(x + -2.222222222) equal to 2.591534175 and -2.591534175.


Subproblem 1
x + -2.222222222 = 2.591534175

Simplifying
x + -2.222222222 = 2.591534175

Reorder the terms:
-2.222222222 + x = 2.591534175

Solving
-2.222222222 + x = 2.591534175

Solving for variable 'x'.

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

Add '2.222222222' to each side of the equation.
-2.222222222 + 2.222222222 + x = 2.591534175 + 2.222222222

Combine like terms: -2.222222222 + 2.222222222 = 0.000000000
0.000000000 + x = 2.591534175 + 2.222222222
x = 2.591534175 + 2.222222222

Combine like terms: 2.591534175 + 2.222222222 = 4.813756397
x = 4.813756397

Simplifying
x = 4.813756397


Subproblem 2
x + -2.222222222 = -2.591534175

Simplifying
x + -2.222222222 = -2.591534175

Reorder the terms:
-2.222222222 + x = -2.591534175

Solving
-2.222222222 + x = -2.591534175

Solving for variable 'x'.

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

Add '2.222222222' to each side of the equation.
-2.222222222 + 2.222222222 + x = -2.591534175 + 2.222222222

Combine like terms: -2.222222222 + 2.222222222 = 0.000000000
0.000000000 + x = -2.591534175 + 2.222222222
x = -2.591534175 + 2.222222222

Combine like terms: -2.591534175 + 2.222222222 = -0.369311953
x = -0.369311953

Simplifying
x = -0.369311953


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.813756397, -0.369311953}

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