-0.1x^2+1.1x-2.8=0

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Solution for -0.1x^2+1.1x-2.8=0 equation:


Simplifying
-0.1x2 + 1.1x + -2.8 = 0

Reorder the terms:
-2.8 + 1.1x + -0.1x2 = 0

Solving
-2.8 + 1.1x + -0.1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.1 the coefficient of the squared term: 

Divide each side by '-0.1'.
28 + -11x + x2 = 0

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + -11x + -28 + x2 = 0 + -28

Reorder the terms:
28 + -28 + -11x + x2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -11x + x2 = 0 + -28
-11x + x2 = 0 + -28

Combine like terms: 0 + -28 = -28
-11x + x2 = -28

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = -28 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -28 + 30.25

Combine like terms: -28 + 30.25 = 2.25
30.25 + -11x + x2 = 2.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 2.25

Calculate the square root of the right side: 1.5

Break this problem into two subproblems by setting 
(x + -5.5) equal to 1.5 and -1.5.

Subproblem 1

x + -5.5 = 1.5 Simplifying x + -5.5 = 1.5 Reorder the terms: -5.5 + x = 1.5 Solving -5.5 + x = 1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 1.5 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 1.5 + 5.5 x = 1.5 + 5.5 Combine like terms: 1.5 + 5.5 = 7 x = 7 Simplifying x = 7

Subproblem 2

x + -5.5 = -1.5 Simplifying x + -5.5 = -1.5 Reorder the terms: -5.5 + x = -1.5 Solving -5.5 + x = -1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -1.5 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -1.5 + 5.5 x = -1.5 + 5.5 Combine like terms: -1.5 + 5.5 = 4 x = 4 Simplifying x = 4

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7, 4}

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