y^2-17y+10=0

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Solution for y^2-17y+10=0 equation:


Simplifying
y2 + -17y + 10 = 0

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

Solving
10 + -17y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -17y + -10 + y2 = 0 + -10

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

Combine like terms: 10 + -10 = 0
0 + -17y + y2 = 0 + -10
-17y + y2 = 0 + -10

Combine like terms: 0 + -10 = -10
-17y + y2 = -10

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 = -10 + 72.25

Reorder the terms:
72.25 + -17y + y2 = -10 + 72.25

Combine like terms: -10 + 72.25 = 62.25
72.25 + -17y + y2 = 62.25

Factor a perfect square on the left side:
(y + -8.5)(y + -8.5) = 62.25

Calculate the square root of the right side: 7.889866919

Break this problem into two subproblems by setting 
(y + -8.5) equal to 7.889866919 and -7.889866919.


Subproblem 1
y + -8.5 = 7.889866919

Simplifying
y + -8.5 = 7.889866919

Reorder the terms:
-8.5 + y = 7.889866919

Solving
-8.5 + y = 7.889866919

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 = 7.889866919 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + y = 7.889866919 + 8.5
y = 7.889866919 + 8.5

Combine like terms: 7.889866919 + 8.5 = 16.389866919
y = 16.389866919

Simplifying
y = 16.389866919


Subproblem 2
y + -8.5 = -7.889866919

Simplifying
y + -8.5 = -7.889866919

Reorder the terms:
-8.5 + y = -7.889866919

Solving
-8.5 + y = -7.889866919

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 = -7.889866919 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + y = -7.889866919 + 8.5
y = -7.889866919 + 8.5

Combine like terms: -7.889866919 + 8.5 = 0.610133081
y = 0.610133081

Simplifying
y = 0.610133081


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {16.389866919, 0.610133081}

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