x^2-2.2x-9.75=0

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Solution for x^2-2.2x-9.75=0 equation: 


Simplifying
x2 + -2.2x + -9.75 = 0

Reorder the terms:
-9.75 + -2.2x + x2 = 0

Solving
-9.75 + -2.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '9.75' to each side of the equation.
-9.75 + -2.2x + 9.75 + x2 = 0 + 9.75

Reorder the terms:
-9.75 + 9.75 + -2.2x + x2 = 0 + 9.75

Combine like terms: -9.75 + 9.75 = 0.00
0.00 + -2.2x + x2 = 0 + 9.75
-2.2x + x2 = 0 + 9.75

Combine like terms: 0 + 9.75 = 9.75
-2.2x + x2 = 9.75

The x term is -2.2x.  Take half its coefficient (-1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
-2.2x + 1.21 + x2 = 9.75 + 1.21

Reorder the terms:
1.21 + -2.2x + x2 = 9.75 + 1.21

Combine like terms: 9.75 + 1.21 = 10.96
1.21 + -2.2x + x2 = 10.96

Factor a perfect square on the left side:
(x + -1.1)(x + -1.1) = 10.96

Calculate the square root of the right side: 3.310589071

Break this problem into two subproblems by setting 
(x + -1.1) equal to 3.310589071 and -3.310589071.


Subproblem 1
x + -1.1 = 3.310589071

Simplifying
x + -1.1 = 3.310589071

Reorder the terms:
-1.1 + x = 3.310589071

Solving
-1.1 + x = 3.310589071

Solving for variable 'x'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + x = 3.310589071 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + x = 3.310589071 + 1.1
x = 3.310589071 + 1.1

Combine like terms: 3.310589071 + 1.1 = 4.410589071
x = 4.410589071

Simplifying
x = 4.410589071


Subproblem 2
x + -1.1 = -3.310589071

Simplifying
x + -1.1 = -3.310589071

Reorder the terms:
-1.1 + x = -3.310589071

Solving
-1.1 + x = -3.310589071

Solving for variable 'x'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + x = -3.310589071 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + x = -3.310589071 + 1.1
x = -3.310589071 + 1.1

Combine like terms: -3.310589071 + 1.1 = -2.210589071
x = -2.210589071

Simplifying
x = -2.210589071


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.410589071, -2.210589071}

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