-0.4x^2+2.2x+4.7=0

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Solution for -0.4x^2+2.2x+4.7=0 equation: 


Simplifying
-0.4x2 + 2.2x + 4.7 = 0

Reorder the terms:
4.7 + 2.2x + -0.4x2 = 0

Solving
4.7 + 2.2x + -0.4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.4 the coefficient of the squared term: 

Divide each side by '-0.4'.
-11.75 + -5.5x + x2 = 0

Move the constant term to the right:

Add '11.75' to each side of the equation.
-11.75 + -5.5x + 11.75 + x2 = 0 + 11.75

Reorder the terms:
-11.75 + 11.75 + -5.5x + x2 = 0 + 11.75

Combine like terms: -11.75 + 11.75 = 0.00
0.00 + -5.5x + x2 = 0 + 11.75
-5.5x + x2 = 0 + 11.75

Combine like terms: 0 + 11.75 = 11.75
-5.5x + x2 = 11.75

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = 11.75 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 11.75 + 7.5625

Combine like terms: 11.75 + 7.5625 = 19.3125
7.5625 + -5.5x + x2 = 19.3125

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 19.3125

Calculate the square root of the right side: 4.394598958

Break this problem into two subproblems by setting 
(x + -2.75) equal to 4.394598958 and -4.394598958.


Subproblem 1
x + -2.75 = 4.394598958

Simplifying
x + -2.75 = 4.394598958

Reorder the terms:
-2.75 + x = 4.394598958

Solving
-2.75 + x = 4.394598958

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = 4.394598958 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 4.394598958 + 2.75
x = 4.394598958 + 2.75

Combine like terms: 4.394598958 + 2.75 = 7.144598958
x = 7.144598958

Simplifying
x = 7.144598958


Subproblem 2
x + -2.75 = -4.394598958

Simplifying
x + -2.75 = -4.394598958

Reorder the terms:
-2.75 + x = -4.394598958

Solving
-2.75 + x = -4.394598958

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = -4.394598958 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -4.394598958 + 2.75
x = -4.394598958 + 2.75

Combine like terms: -4.394598958 + 2.75 = -1.644598958
x = -1.644598958

Simplifying
x = -1.644598958


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.144598958, -1.644598958}

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