2y^2-11y+19=(y-5)2

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Solution for 2y^2-11y+19=(y-5)2 equation: 


Simplifying
2y2 + -11y + 19 = (y + -5) * 2

Reorder the terms:
19 + -11y + 2y2 = (y + -5) * 2

Reorder the terms:
19 + -11y + 2y2 = (-5 + y) * 2

Reorder the terms for easier multiplication:
19 + -11y + 2y2 = 2(-5 + y)
19 + -11y + 2y2 = (-5 * 2 + y * 2)
19 + -11y + 2y2 = (-10 + 2y)

Solving
19 + -11y + 2y2 = -10 + 2y

Solving for variable 'y'.

Reorder the terms:
19 + 10 + -11y + -2y + 2y2 = -10 + 2y + 10 + -2y

Combine like terms: 19 + 10 = 29
29 + -11y + -2y + 2y2 = -10 + 2y + 10 + -2y

Combine like terms: -11y + -2y = -13y
29 + -13y + 2y2 = -10 + 2y + 10 + -2y

Reorder the terms:
29 + -13y + 2y2 = -10 + 10 + 2y + -2y

Combine like terms: -10 + 10 = 0
29 + -13y + 2y2 = 0 + 2y + -2y
29 + -13y + 2y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
29 + -13y + 2y2 = 0

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

Divide each side by '2'.
14.5 + -6.5y + y2 = 0

Move the constant term to the right:

Add '-14.5' to each side of the equation.
14.5 + -6.5y + -14.5 + y2 = 0 + -14.5

Reorder the terms:
14.5 + -14.5 + -6.5y + y2 = 0 + -14.5

Combine like terms: 14.5 + -14.5 = 0.0
0.0 + -6.5y + y2 = 0 + -14.5
-6.5y + y2 = 0 + -14.5

Combine like terms: 0 + -14.5 = -14.5
-6.5y + y2 = -14.5

The y term is -6.5y.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5y + 10.5625 + y2 = -14.5 + 10.5625

Reorder the terms:
10.5625 + -6.5y + y2 = -14.5 + 10.5625

Combine like terms: -14.5 + 10.5625 = -3.9375
10.5625 + -6.5y + y2 = -3.9375

Factor a perfect square on the left side:
(y + -3.25)(y + -3.25) = -3.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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