(-.8x^2)+2.2x+9=0

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Solution for (-.8x^2)+2.2x+9=0 equation:


Simplifying
(-0.8x2) + 2.2x + 9 = 0

Reorder the terms:
9 + 2.2x + (-0.8x2) = 0

Solving
9 + 2.2x + (-0.8x2) = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.8 the coefficient of the squared term: 

Divide each side by '-0.8'.
-11.25 + -2.75x + x2 = 0

Move the constant term to the right:

Add '11.25' to each side of the equation.
-11.25 + -2.75x + 11.25 + x2 = 0 + 11.25

Reorder the terms:
-11.25 + 11.25 + -2.75x + x2 = 0 + 11.25

Combine like terms: -11.25 + 11.25 = 0.00
0.00 + -2.75x + x2 = 0 + 11.25
-2.75x + x2 = 0 + 11.25

Combine like terms: 0 + 11.25 = 11.25
-2.75x + x2 = 11.25

The x term is -2.75x.  Take half its coefficient (-1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
-2.75x + 1.890625 + x2 = 11.25 + 1.890625

Reorder the terms:
1.890625 + -2.75x + x2 = 11.25 + 1.890625

Combine like terms: 11.25 + 1.890625 = 13.140625
1.890625 + -2.75x + x2 = 13.140625

Factor a perfect square on the left side:
((x) + -1.375)((x) + -1.375) = 13.140625

Calculate the square root of the right side: 3.625

Break this problem into two subproblems by setting 
((x) + -1.375) equal to 3.625 and -3.625.

Subproblem 1

(x) + -1.375 = 3.625 Simplifying (x) + -1.375 = 3.625 x + -1.375 = 3.625 Reorder the terms: -1.375 + x = 3.625 Solving -1.375 + x = 3.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 3.625 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 3.625 + 1.375 x = 3.625 + 1.375 Combine like terms: 3.625 + 1.375 = 5 x = 5 Simplifying x = 5

Subproblem 2

(x) + -1.375 = -3.625 Simplifying (x) + -1.375 = -3.625 x + -1.375 = -3.625 Reorder the terms: -1.375 + x = -3.625 Solving -1.375 + x = -3.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -3.625 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -3.625 + 1.375 x = -3.625 + 1.375 Combine like terms: -3.625 + 1.375 = -2.25 x = -2.25 Simplifying x = -2.25

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5, -2.25}

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