(2.89-y^2)=(y-1.7)

Solution for (2.89-y^2)=(y-1.7) equation:

Simplifying
(2.89 + -1y2) = (y + -1.7)

Remove parenthesis around (2.89 + -1y2)
2.89 + -1y2 = (y + -1.7)

Reorder the terms:
2.89 + -1y2 = (-1.7 + y)

Remove parenthesis around (-1.7 + y)
2.89 + -1y2 = -1.7 + y

Solving
2.89 + -1y2 = -1.7 + y

Solving for variable 'y'.

Reorder the terms:
2.89 + 1.7 + -1y + -1y2 = -1.7 + y + 1.7 + -1y

Combine like terms: 2.89 + 1.7 = 4.59
4.59 + -1y + -1y2 = -1.7 + y + 1.7 + -1y

Reorder the terms:
4.59 + -1y + -1y2 = -1.7 + 1.7 + y + -1y

Combine like terms: -1.7 + 1.7 = 0.0
4.59 + -1y + -1y2 = 0.0 + y + -1y
4.59 + -1y + -1y2 = y + -1y

Combine like terms: y + -1y = 0
4.59 + -1y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-4.59 + y + y2 = 0

Move the constant term to the right:

Add '4.59' to each side of the equation.
-4.59 + y + 4.59 + y2 = 0 + 4.59

Reorder the terms:
-4.59 + 4.59 + y + y2 = 0 + 4.59

Combine like terms: -4.59 + 4.59 = 0.00
0.00 + y + y2 = 0 + 4.59
y + y2 = 0 + 4.59

Combine like terms: 0 + 4.59 = 4.59
y + y2 = 4.59

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + y2 = 4.59 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + y2 = 4.59 + 0.25

Combine like terms: 4.59 + 0.25 = 4.84
1.25 + y2 = 4.84

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 4.84

Calculate the square root of the right side: 2.2

Break this problem into two subproblems by setting 
(y + 0.5) equal to 2.2 and -2.2.

Subproblem 1
y + 0.5 = 2.2

Simplifying
y + 0.5 = 2.2

Reorder the terms:
0.5 + y = 2.2

Solving
0.5 + y = 2.2

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = 2.2 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 2.2 + -0.5
y = 2.2 + -0.5

Combine like terms: 2.2 + -0.5 = 1.7
y = 1.7

Simplifying
y = 1.7

Subproblem 2
y + 0.5 = -2.2

Simplifying
y + 0.5 = -2.2

Reorder the terms:
0.5 + y = -2.2

Solving
0.5 + y = -2.2

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = -2.2 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -2.2 + -0.5
y = -2.2 + -0.5

Combine like terms: -2.2 + -0.5 = -2.7
y = -2.7

Simplifying
y = -2.7

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.7, -2.7}