-0.05x^2-5.5x-1=0

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Solution for -0.05x^2-5.5x-1=0 equation:


Simplifying
-0.05x2 + -5.5x + -1 = 0

Reorder the terms:
-1 + -5.5x + -0.05x2 = 0

Solving
-1 + -5.5x + -0.05x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.05 the coefficient of the squared term: 

Divide each side by '-0.05'.
20 + 110x + x2 = 0

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + 110x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + 110x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 110x + x2 = 0 + -20
110x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
110x + x2 = -20

The x term is 110x.  Take half its coefficient (55).
Square it (3025) and add it to both sides.

Add '3025' to each side of the equation.
110x + 3025 + x2 = -20 + 3025

Reorder the terms:
3025 + 110x + x2 = -20 + 3025

Combine like terms: -20 + 3025 = 3005
3025 + 110x + x2 = 3005

Factor a perfect square on the left side:
(x + 55)(x + 55) = 3005

Calculate the square root of the right side: 54.817880295

Break this problem into two subproblems by setting 
(x + 55) equal to 54.817880295 and -54.817880295.

Subproblem 1

x + 55 = 54.817880295 Simplifying x + 55 = 54.817880295 Reorder the terms: 55 + x = 54.817880295 Solving 55 + x = 54.817880295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-55' to each side of the equation. 55 + -55 + x = 54.817880295 + -55 Combine like terms: 55 + -55 = 0 0 + x = 54.817880295 + -55 x = 54.817880295 + -55 Combine like terms: 54.817880295 + -55 = -0.182119705 x = -0.182119705 Simplifying x = -0.182119705

Subproblem 2

x + 55 = -54.817880295 Simplifying x + 55 = -54.817880295 Reorder the terms: 55 + x = -54.817880295 Solving 55 + x = -54.817880295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-55' to each side of the equation. 55 + -55 + x = -54.817880295 + -55 Combine like terms: 55 + -55 = 0 0 + x = -54.817880295 + -55 x = -54.817880295 + -55 Combine like terms: -54.817880295 + -55 = -109.817880295 x = -109.817880295 Simplifying x = -109.817880295

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.182119705, -109.817880295}

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