10y^2+17y+2=

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Solution for 10y^2+17y+2= equation: 


Simplifying
10y2 + 17y + 2 = 0

Reorder the terms:
2 + 17y + 10y2 = 0

Solving
2 + 17y + 10y2 = 0

Solving for variable 'y'.

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

Divide each side by '10'.
0.2 + 1.7y + y2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 1.7y + -0.2 + y2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 1.7y + y2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 1.7y + y2 = 0 + -0.2
1.7y + y2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
1.7y + y2 = -0.2

The y term is 1.7y.  Take half its coefficient (0.85).
Square it (0.7225) and add it to both sides.

Add '0.7225' to each side of the equation.
1.7y + 0.7225 + y2 = -0.2 + 0.7225

Reorder the terms:
0.7225 + 1.7y + y2 = -0.2 + 0.7225

Combine like terms: -0.2 + 0.7225 = 0.5225
0.7225 + 1.7y + y2 = 0.5225

Factor a perfect square on the left side:
(y + 0.85)(y + 0.85) = 0.5225

Calculate the square root of the right side: 0.722841615

Break this problem into two subproblems by setting 
(y + 0.85) equal to 0.722841615 and -0.722841615.


Subproblem 1
y + 0.85 = 0.722841615

Simplifying
y + 0.85 = 0.722841615

Reorder the terms:
0.85 + y = 0.722841615

Solving
0.85 + y = 0.722841615

Solving for variable 'y'.

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

Add '-0.85' to each side of the equation.
0.85 + -0.85 + y = 0.722841615 + -0.85

Combine like terms: 0.85 + -0.85 = 0.00
0.00 + y = 0.722841615 + -0.85
y = 0.722841615 + -0.85

Combine like terms: 0.722841615 + -0.85 = -0.127158385
y = -0.127158385

Simplifying
y = -0.127158385


Subproblem 2
y + 0.85 = -0.722841615

Simplifying
y + 0.85 = -0.722841615

Reorder the terms:
0.85 + y = -0.722841615

Solving
0.85 + y = -0.722841615

Solving for variable 'y'.

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

Add '-0.85' to each side of the equation.
0.85 + -0.85 + y = -0.722841615 + -0.85

Combine like terms: 0.85 + -0.85 = 0.00
0.00 + y = -0.722841615 + -0.85
y = -0.722841615 + -0.85

Combine like terms: -0.722841615 + -0.85 = -1.572841615
y = -1.572841615

Simplifying
y = -1.572841615


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.127158385, -1.572841615}

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