16.5*x-0.98*(x^2)-24.22=0

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Solution for 16.5*x-0.98*(x^2)-24.22=0 equation: 


Simplifying
16.5x + -0.98(x2) + -24.22 = 0

Reorder the terms:
-24.22 + 16.5x + -0.98x2 = 0

Solving
-24.22 + 16.5x + -0.98x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.98 the coefficient of the squared term: 

Divide each side by '-0.98'.
24.71428571 + -16.83673469x + x2 = 0

Move the constant term to the right:

Add '-24.71428571' to each side of the equation.
24.71428571 + -16.83673469x + -24.71428571 + x2 = 0 + -24.71428571

Reorder the terms:
24.71428571 + -24.71428571 + -16.83673469x + x2 = 0 + -24.71428571

Combine like terms: 24.71428571 + -24.71428571 = 0.00000000
0.00000000 + -16.83673469x + x2 = 0 + -24.71428571
-16.83673469x + x2 = 0 + -24.71428571

Combine like terms: 0 + -24.71428571 = -24.71428571
-16.83673469x + x2 = -24.71428571

The x term is -16.83673469x.  Take half its coefficient (-8.418367345).
Square it (70.86890876) and add it to both sides.

Add '70.86890876' to each side of the equation.
-16.83673469x + 70.86890876 + x2 = -24.71428571 + 70.86890876

Reorder the terms:
70.86890876 + -16.83673469x + x2 = -24.71428571 + 70.86890876

Combine like terms: -24.71428571 + 70.86890876 = 46.15462305
70.86890876 + -16.83673469x + x2 = 46.15462305

Factor a perfect square on the left side:
(x + -8.418367345)(x + -8.418367345) = 46.15462305

Calculate the square root of the right side: 6.793719383

Break this problem into two subproblems by setting 
(x + -8.418367345) equal to 6.793719383 and -6.793719383.


Subproblem 1
x + -8.418367345 = 6.793719383

Simplifying
x + -8.418367345 = 6.793719383

Reorder the terms:
-8.418367345 + x = 6.793719383

Solving
-8.418367345 + x = 6.793719383

Solving for variable 'x'.

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

Add '8.418367345' to each side of the equation.
-8.418367345 + 8.418367345 + x = 6.793719383 + 8.418367345

Combine like terms: -8.418367345 + 8.418367345 = 0.000000000
0.000000000 + x = 6.793719383 + 8.418367345
x = 6.793719383 + 8.418367345

Combine like terms: 6.793719383 + 8.418367345 = 15.212086728
x = 15.212086728

Simplifying
x = 15.212086728


Subproblem 2
x + -8.418367345 = -6.793719383

Simplifying
x + -8.418367345 = -6.793719383

Reorder the terms:
-8.418367345 + x = -6.793719383

Solving
-8.418367345 + x = -6.793719383

Solving for variable 'x'.

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

Add '8.418367345' to each side of the equation.
-8.418367345 + 8.418367345 + x = -6.793719383 + 8.418367345

Combine like terms: -8.418367345 + 8.418367345 = 0.000000000
0.000000000 + x = -6.793719383 + 8.418367345
x = -6.793719383 + 8.418367345

Combine like terms: -6.793719383 + 8.418367345 = 1.624647962
x = 1.624647962

Simplifying
x = 1.624647962


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.212086728, 1.624647962}

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