y(y+3)=17

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Solution for y(y+3)=17 equation:


Simplifying
y(y + 3) = 17

Reorder the terms:
y(3 + y) = 17
(3 * y + y * y) = 17
(3y + y2) = 17

Solving
3y + y2 = 17

Solving for variable 'y'.

Reorder the terms:
-17 + 3y + y2 = 17 + -17

Combine like terms: 17 + -17 = 0
-17 + 3y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 3y + 17 + y2 = 0 + 17

Reorder the terms:
-17 + 17 + 3y + y2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 3y + y2 = 0 + 17
3y + y2 = 0 + 17

Combine like terms: 0 + 17 = 17
3y + y2 = 17

The y term is 3y.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3y + 2.25 + y2 = 17 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 17 + 2.25

Combine like terms: 17 + 2.25 = 19.25
2.25 + 3y + y2 = 19.25

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(y + 1.5) equal to 4.387482194 and -4.387482194.


Subproblem 1
y + 1.5 = 4.387482194

Simplifying
y + 1.5 = 4.387482194

Reorder the terms:
1.5 + y = 4.387482194

Solving
1.5 + y = 4.387482194

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = 4.387482194 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = 4.387482194 + -1.5
y = 4.387482194 + -1.5

Combine like terms: 4.387482194 + -1.5 = 2.887482194
y = 2.887482194

Simplifying
y = 2.887482194


Subproblem 2
y + 1.5 = -4.387482194

Simplifying
y + 1.5 = -4.387482194

Reorder the terms:
1.5 + y = -4.387482194

Solving
1.5 + y = -4.387482194

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = -4.387482194 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = -4.387482194 + -1.5
y = -4.387482194 + -1.5

Combine like terms: -4.387482194 + -1.5 = -5.887482194
y = -5.887482194

Simplifying
y = -5.887482194


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.887482194, -5.887482194}

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