x^2-2.2x-4=0

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Solution for x^2-2.2x-4=0 equation:


Simplifying
x2 + -2.2x + -4 = 0

Reorder the terms:
-4 + -2.2x + x2 = 0

Solving
-4 + -2.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -2.2x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -2.2x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -2.2x + x2 = 0 + 4
-2.2x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-2.2x + x2 = 4

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 = 4 + 1.21

Reorder the terms:
1.21 + -2.2x + x2 = 4 + 1.21

Combine like terms: 4 + 1.21 = 5.21
1.21 + -2.2x + x2 = 5.21

Factor a perfect square on the left side:
(x + -1.1)(x + -1.1) = 5.21

Calculate the square root of the right side: 2.282542442

Break this problem into two subproblems by setting 
(x + -1.1) equal to 2.282542442 and -2.282542442.

Subproblem 1

x + -1.1 = 2.282542442 Simplifying x + -1.1 = 2.282542442 Reorder the terms: -1.1 + x = 2.282542442 Solving -1.1 + x = 2.282542442 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 = 2.282542442 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = 2.282542442 + 1.1 x = 2.282542442 + 1.1 Combine like terms: 2.282542442 + 1.1 = 3.382542442 x = 3.382542442 Simplifying x = 3.382542442

Subproblem 2

x + -1.1 = -2.282542442 Simplifying x + -1.1 = -2.282542442 Reorder the terms: -1.1 + x = -2.282542442 Solving -1.1 + x = -2.282542442 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 = -2.282542442 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = -2.282542442 + 1.1 x = -2.282542442 + 1.1 Combine like terms: -2.282542442 + 1.1 = -1.182542442 x = -1.182542442 Simplifying x = -1.182542442

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.382542442, -1.182542442}

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