-0.2x^2+0.7x+0.9=0

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Solution for -0.2x^2+0.7x+0.9=0 equation: 


Simplifying
-0.2x2 + 0.7x + 0.9 = 0

Reorder the terms:
0.9 + 0.7x + -0.2x2 = 0

Solving
0.9 + 0.7x + -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'.
-4.5 + -3.5x + x2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -3.5x + 4.5 + x2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -3.5x + x2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -3.5x + x2 = 0 + 4.5
-3.5x + x2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-3.5x + x2 = 4.5

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = 4.5 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 4.5 + 3.0625

Combine like terms: 4.5 + 3.0625 = 7.5625
3.0625 + -3.5x + x2 = 7.5625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 7.5625

Calculate the square root of the right side: 2.75

Break this problem into two subproblems by setting 
(x + -1.75) equal to 2.75 and -2.75.


Subproblem 1
x + -1.75 = 2.75

Simplifying
x + -1.75 = 2.75

Reorder the terms:
-1.75 + x = 2.75

Solving
-1.75 + x = 2.75

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = 2.75 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 2.75 + 1.75
x = 2.75 + 1.75

Combine like terms: 2.75 + 1.75 = 4.5
x = 4.5

Simplifying
x = 4.5


Subproblem 2
x + -1.75 = -2.75

Simplifying
x + -1.75 = -2.75

Reorder the terms:
-1.75 + x = -2.75

Solving
-1.75 + x = -2.75

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = -2.75 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -2.75 + 1.75
x = -2.75 + 1.75

Combine like terms: -2.75 + 1.75 = -1
x = -1

Simplifying
x = -1


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.5, -1}

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