-4.9x^2+24.5x+9.9=0

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Solution for -4.9x^2+24.5x+9.9=0 equation: 


Simplifying
-4.9x2 + 24.5x + 9.9 = 0

Reorder the terms:
9.9 + 24.5x + -4.9x2 = 0

Solving
9.9 + 24.5x + -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'.
-2.020408163 + -5x + x2 = 0

Move the constant term to the right:

Add '2.020408163' to each side of the equation.
-2.020408163 + -5x + 2.020408163 + x2 = 0 + 2.020408163

Reorder the terms:
-2.020408163 + 2.020408163 + -5x + x2 = 0 + 2.020408163

Combine like terms: -2.020408163 + 2.020408163 = 0.000000000
0.000000000 + -5x + x2 = 0 + 2.020408163
-5x + x2 = 0 + 2.020408163

Combine like terms: 0 + 2.020408163 = 2.020408163
-5x + x2 = 2.020408163

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 2.020408163 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 2.020408163 + 6.25

Combine like terms: 2.020408163 + 6.25 = 8.270408163
6.25 + -5x + x2 = 8.270408163

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 8.270408163

Calculate the square root of the right side: 2.875831734

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.875831734 and -2.875831734.


Subproblem 1
x + -2.5 = 2.875831734

Simplifying
x + -2.5 = 2.875831734

Reorder the terms:
-2.5 + x = 2.875831734

Solving
-2.5 + x = 2.875831734

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 2.875831734 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.875831734 + 2.5
x = 2.875831734 + 2.5

Combine like terms: 2.875831734 + 2.5 = 5.375831734
x = 5.375831734

Simplifying
x = 5.375831734


Subproblem 2
x + -2.5 = -2.875831734

Simplifying
x + -2.5 = -2.875831734

Reorder the terms:
-2.5 + x = -2.875831734

Solving
-2.5 + x = -2.875831734

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -2.875831734 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.875831734 + 2.5
x = -2.875831734 + 2.5

Combine like terms: -2.875831734 + 2.5 = -0.375831734
x = -0.375831734

Simplifying
x = -0.375831734


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.375831734, -0.375831734}

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