-4.9x^2+80x+224=0

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Solution for -4.9x^2+80x+224=0 equation: 


Simplifying
-4.9x2 + 80x + 224 = 0

Reorder the terms:
224 + 80x + -4.9x2 = 0

Solving
224 + 80x + -4.9x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
-45.71428571 + -16.32653061x + x2 = 0

Move the constant term to the right:

Add '45.71428571' to each side of the equation.
-45.71428571 + -16.32653061x + 45.71428571 + x2 = 0 + 45.71428571

Reorder the terms:
-45.71428571 + 45.71428571 + -16.32653061x + x2 = 0 + 45.71428571

Combine like terms: -45.71428571 + 45.71428571 = 0.00000000
0.00000000 + -16.32653061x + x2 = 0 + 45.71428571
-16.32653061x + x2 = 0 + 45.71428571

Combine like terms: 0 + 45.71428571 = 45.71428571
-16.32653061x + x2 = 45.71428571

The x term is -16.32653061x.  Take half its coefficient (-8.163265305).
Square it (66.63890044) and add it to both sides.

Add '66.63890044' to each side of the equation.
-16.32653061x + 66.63890044 + x2 = 45.71428571 + 66.63890044

Reorder the terms:
66.63890044 + -16.32653061x + x2 = 45.71428571 + 66.63890044

Combine like terms: 45.71428571 + 66.63890044 = 112.35318615
66.63890044 + -16.32653061x + x2 = 112.35318615

Factor a perfect square on the left side:
(x + -8.163265305)(x + -8.163265305) = 112.35318615

Calculate the square root of the right side: 10.599678587

Break this problem into two subproblems by setting 
(x + -8.163265305) equal to 10.599678587 and -10.599678587.


Subproblem 1
x + -8.163265305 = 10.599678587

Simplifying
x + -8.163265305 = 10.599678587

Reorder the terms:
-8.163265305 + x = 10.599678587

Solving
-8.163265305 + x = 10.599678587

Solving for variable 'x'.

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

Add '8.163265305' to each side of the equation.
-8.163265305 + 8.163265305 + x = 10.599678587 + 8.163265305

Combine like terms: -8.163265305 + 8.163265305 = 0.000000000
0.000000000 + x = 10.599678587 + 8.163265305
x = 10.599678587 + 8.163265305

Combine like terms: 10.599678587 + 8.163265305 = 18.762943892
x = 18.762943892

Simplifying
x = 18.762943892


Subproblem 2
x + -8.163265305 = -10.599678587

Simplifying
x + -8.163265305 = -10.599678587

Reorder the terms:
-8.163265305 + x = -10.599678587

Solving
-8.163265305 + x = -10.599678587

Solving for variable 'x'.

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

Add '8.163265305' to each side of the equation.
-8.163265305 + 8.163265305 + x = -10.599678587 + 8.163265305

Combine like terms: -8.163265305 + 8.163265305 = 0.000000000
0.000000000 + x = -10.599678587 + 8.163265305
x = -10.599678587 + 8.163265305

Combine like terms: -10.599678587 + 8.163265305 = -2.436413282
x = -2.436413282

Simplifying
x = -2.436413282


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.762943892, -2.436413282}

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