-0.2x^2+0.9x+2.2=0

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Solution for -0.2x^2+0.9x+2.2=0 equation:


Simplifying
-0.2x2 + 0.9x + 2.2 = 0

Reorder the terms:
2.2 + 0.9x + -0.2x2 = 0

Solving
2.2 + 0.9x + -0.2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.2 the coefficient of the squared term: 

Divide each side by '-0.2'.
-11 + -4.5x + x2 = 0

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -4.5x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + -4.5x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -4.5x + x2 = 0 + 11
-4.5x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
-4.5x + x2 = 11

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = 11 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 11 + 5.0625

Combine like terms: 11 + 5.0625 = 16.0625
5.0625 + -4.5x + x2 = 16.0625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 16.0625

Calculate the square root of the right side: 4.007804885

Break this problem into two subproblems by setting 
(x + -2.25) equal to 4.007804885 and -4.007804885.

Subproblem 1

x + -2.25 = 4.007804885 Simplifying x + -2.25 = 4.007804885 Reorder the terms: -2.25 + x = 4.007804885 Solving -2.25 + x = 4.007804885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 4.007804885 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 4.007804885 + 2.25 x = 4.007804885 + 2.25 Combine like terms: 4.007804885 + 2.25 = 6.257804885 x = 6.257804885 Simplifying x = 6.257804885

Subproblem 2

x + -2.25 = -4.007804885 Simplifying x + -2.25 = -4.007804885 Reorder the terms: -2.25 + x = -4.007804885 Solving -2.25 + x = -4.007804885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -4.007804885 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -4.007804885 + 2.25 x = -4.007804885 + 2.25 Combine like terms: -4.007804885 + 2.25 = -1.757804885 x = -1.757804885 Simplifying x = -1.757804885

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.257804885, -1.757804885}

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