44=0.055x^2+1.1x

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Solution for 44=0.055x^2+1.1x equation:


Simplifying
44 = 0.055x2 + 1.1x

Reorder the terms:
44 = 1.1x + 0.055x2

Solving
44 = 1.1x + 0.055x2

Solving for variable 'x'.

Reorder the terms:
44 + -1.1x + -0.055x2 = 1.1x + -1.1x + 0.055x2 + -0.055x2

Combine like terms: 1.1x + -1.1x = 0.0
44 + -1.1x + -0.055x2 = 0.0 + 0.055x2 + -0.055x2
44 + -1.1x + -0.055x2 = 0.055x2 + -0.055x2

Combine like terms: 0.055x2 + -0.055x2 = 0.000
44 + -1.1x + -0.055x2 = 0.000

Begin completing the square.  Divide all terms by
-0.055 the coefficient of the squared term: 

Divide each side by '-0.055'.
-800 + 20x + x2 = 0

Move the constant term to the right:

Add '800' to each side of the equation.
-800 + 20x + 800 + x2 = 0 + 800

Reorder the terms:
-800 + 800 + 20x + x2 = 0 + 800

Combine like terms: -800 + 800 = 0
0 + 20x + x2 = 0 + 800
20x + x2 = 0 + 800

Combine like terms: 0 + 800 = 800
20x + x2 = 800

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 800 + 100

Reorder the terms:
100 + 20x + x2 = 800 + 100

Combine like terms: 800 + 100 = 900
100 + 20x + x2 = 900

Factor a perfect square on the left side:
(x + 10)(x + 10) = 900

Calculate the square root of the right side: 30

Break this problem into two subproblems by setting 
(x + 10) equal to 30 and -30.

Subproblem 1

x + 10 = 30 Simplifying x + 10 = 30 Reorder the terms: 10 + x = 30 Solving 10 + x = 30 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 30 + -10 Combine like terms: 10 + -10 = 0 0 + x = 30 + -10 x = 30 + -10 Combine like terms: 30 + -10 = 20 x = 20 Simplifying x = 20

Subproblem 2

x + 10 = -30 Simplifying x + 10 = -30 Reorder the terms: 10 + x = -30 Solving 10 + x = -30 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -30 + -10 Combine like terms: 10 + -10 = 0 0 + x = -30 + -10 x = -30 + -10 Combine like terms: -30 + -10 = -40 x = -40 Simplifying x = -40

Solution

The solution to the problem is based on the solutions from the subproblems. x = {20, -40}

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