y^2-17y=-21

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Solution for y^2-17y=-21 equation: 


Simplifying
y2 + -17y = -21

Reorder the terms:
-17y + y2 = -21

Solving
-17y + y2 = -21

Solving for variable 'y'.

Reorder the terms:
21 + -17y + y2 = -21 + 21

Combine like terms: -21 + 21 = 0
21 + -17y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + -17y + -21 + y2 = 0 + -21

Reorder the terms:
21 + -21 + -17y + y2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -17y + y2 = 0 + -21
-17y + y2 = 0 + -21

Combine like terms: 0 + -21 = -21
-17y + y2 = -21

The y term is -17y.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17y + 72.25 + y2 = -21 + 72.25

Reorder the terms:
72.25 + -17y + y2 = -21 + 72.25

Combine like terms: -21 + 72.25 = 51.25
72.25 + -17y + y2 = 51.25

Factor a perfect square on the left side:
(y + -8.5)(y + -8.5) = 51.25

Calculate the square root of the right side: 7.158910532

Break this problem into two subproblems by setting 
(y + -8.5) equal to 7.158910532 and -7.158910532.


Subproblem 1
y + -8.5 = 7.158910532

Simplifying
y + -8.5 = 7.158910532

Reorder the terms:
-8.5 + y = 7.158910532

Solving
-8.5 + y = 7.158910532

Solving for variable 'y'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + y = 7.158910532 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + y = 7.158910532 + 8.5
y = 7.158910532 + 8.5

Combine like terms: 7.158910532 + 8.5 = 15.658910532
y = 15.658910532

Simplifying
y = 15.658910532


Subproblem 2
y + -8.5 = -7.158910532

Simplifying
y + -8.5 = -7.158910532

Reorder the terms:
-8.5 + y = -7.158910532

Solving
-8.5 + y = -7.158910532

Solving for variable 'y'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + y = -7.158910532 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + y = -7.158910532 + 8.5
y = -7.158910532 + 8.5

Combine like terms: -7.158910532 + 8.5 = 1.341089468
y = 1.341089468

Simplifying
y = 1.341089468


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {15.658910532, 1.341089468}

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