4.9x^2-19.6x+9.5=0

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Solution for 4.9x^2-19.6x+9.5=0 equation: 


Simplifying
4.9x2 + -19.6x + 9.5 = 0

Reorder the terms:
9.5 + -19.6x + 4.9x2 = 0

Solving
9.5 + -19.6x + 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'.
1.93877551 + -4x + x2 = 0

Move the constant term to the right:

Add '-1.93877551' to each side of the equation.
1.93877551 + -4x + -1.93877551 + x2 = 0 + -1.93877551

Reorder the terms:
1.93877551 + -1.93877551 + -4x + x2 = 0 + -1.93877551

Combine like terms: 1.93877551 + -1.93877551 = 0.00000000
0.00000000 + -4x + x2 = 0 + -1.93877551
-4x + x2 = 0 + -1.93877551

Combine like terms: 0 + -1.93877551 = -1.93877551
-4x + x2 = -1.93877551

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -1.93877551 + 4

Reorder the terms:
4 + -4x + x2 = -1.93877551 + 4

Combine like terms: -1.93877551 + 4 = 2.06122449
4 + -4x + x2 = 2.06122449

Factor a perfect square on the left side:
(x + -2)(x + -2) = 2.06122449

Calculate the square root of the right side: 1.435696517

Break this problem into two subproblems by setting 
(x + -2) equal to 1.435696517 and -1.435696517.


Subproblem 1
x + -2 = 1.435696517

Simplifying
x + -2 = 1.435696517

Reorder the terms:
-2 + x = 1.435696517

Solving
-2 + x = 1.435696517

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 1.435696517 + 2

Combine like terms: -2 + 2 = 0
0 + x = 1.435696517 + 2
x = 1.435696517 + 2

Combine like terms: 1.435696517 + 2 = 3.435696517
x = 3.435696517

Simplifying
x = 3.435696517


Subproblem 2
x + -2 = -1.435696517

Simplifying
x + -2 = -1.435696517

Reorder the terms:
-2 + x = -1.435696517

Solving
-2 + x = -1.435696517

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -1.435696517 + 2

Combine like terms: -2 + 2 = 0
0 + x = -1.435696517 + 2
x = -1.435696517 + 2

Combine like terms: -1.435696517 + 2 = 0.564303483
x = 0.564303483

Simplifying
x = 0.564303483


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.435696517, 0.564303483}

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