20x^2-44x=-1

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Solution for 20x^2-44x=-1 equation:


Simplifying
20x2 + -44x = -1

Reorder the terms:
-44x + 20x2 = -1

Solving
-44x + 20x2 = -1

Solving for variable 'x'.

Reorder the terms:
1 + -44x + 20x2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -44x + 20x2 = 0

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

Divide each side by '20'.
0.05 + -2.2x + x2 = 0

Move the constant term to the right:

Add '-0.05' to each side of the equation.
0.05 + -2.2x + -0.05 + x2 = 0 + -0.05

Reorder the terms:
0.05 + -0.05 + -2.2x + x2 = 0 + -0.05

Combine like terms: 0.05 + -0.05 = 0.00
0.00 + -2.2x + x2 = 0 + -0.05
-2.2x + x2 = 0 + -0.05

Combine like terms: 0 + -0.05 = -0.05
-2.2x + x2 = -0.05

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 = -0.05 + 1.21

Reorder the terms:
1.21 + -2.2x + x2 = -0.05 + 1.21

Combine like terms: -0.05 + 1.21 = 1.16
1.21 + -2.2x + x2 = 1.16

Factor a perfect square on the left side:
(x + -1.1)(x + -1.1) = 1.16

Calculate the square root of the right side: 1.077032961

Break this problem into two subproblems by setting 
(x + -1.1) equal to 1.077032961 and -1.077032961.

Subproblem 1

x + -1.1 = 1.077032961 Simplifying x + -1.1 = 1.077032961 Reorder the terms: -1.1 + x = 1.077032961 Solving -1.1 + x = 1.077032961 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 = 1.077032961 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = 1.077032961 + 1.1 x = 1.077032961 + 1.1 Combine like terms: 1.077032961 + 1.1 = 2.177032961 x = 2.177032961 Simplifying x = 2.177032961

Subproblem 2

x + -1.1 = -1.077032961 Simplifying x + -1.1 = -1.077032961 Reorder the terms: -1.1 + x = -1.077032961 Solving -1.1 + x = -1.077032961 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 = -1.077032961 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = -1.077032961 + 1.1 x = -1.077032961 + 1.1 Combine like terms: -1.077032961 + 1.1 = 0.022967039 x = 0.022967039 Simplifying x = 0.022967039

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.177032961, 0.022967039}

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