x^2-21x+9.8=0

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Solution for x^2-21x+9.8=0 equation: 


Simplifying
x2 + -21x + 9.8 = 0

Reorder the terms:
9.8 + -21x + x2 = 0

Solving
9.8 + -21x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-9.8' to each side of the equation.
9.8 + -21x + -9.8 + x2 = 0 + -9.8

Reorder the terms:
9.8 + -9.8 + -21x + x2 = 0 + -9.8

Combine like terms: 9.8 + -9.8 = 0.0
0.0 + -21x + x2 = 0 + -9.8
-21x + x2 = 0 + -9.8

Combine like terms: 0 + -9.8 = -9.8
-21x + x2 = -9.8

The x term is -21x.  Take half its coefficient (-10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
-21x + 110.25 + x2 = -9.8 + 110.25

Reorder the terms:
110.25 + -21x + x2 = -9.8 + 110.25

Combine like terms: -9.8 + 110.25 = 100.45
110.25 + -21x + x2 = 100.45

Factor a perfect square on the left side:
(x + -10.5)(x + -10.5) = 100.45

Calculate the square root of the right side: 10.022474744

Break this problem into two subproblems by setting 
(x + -10.5) equal to 10.022474744 and -10.022474744.


Subproblem 1
x + -10.5 = 10.022474744

Simplifying
x + -10.5 = 10.022474744

Reorder the terms:
-10.5 + x = 10.022474744

Solving
-10.5 + x = 10.022474744

Solving for variable 'x'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + x = 10.022474744 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = 10.022474744 + 10.5
x = 10.022474744 + 10.5

Combine like terms: 10.022474744 + 10.5 = 20.522474744
x = 20.522474744

Simplifying
x = 20.522474744


Subproblem 2
x + -10.5 = -10.022474744

Simplifying
x + -10.5 = -10.022474744

Reorder the terms:
-10.5 + x = -10.022474744

Solving
-10.5 + x = -10.022474744

Solving for variable 'x'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + x = -10.022474744 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = -10.022474744 + 10.5
x = -10.022474744 + 10.5

Combine like terms: -10.022474744 + 10.5 = 0.477525256
x = 0.477525256

Simplifying
x = 0.477525256


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.522474744, 0.477525256}

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