y^2-20y+27=0

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Solution for y^2-20y+27=0 equation:


Simplifying
y2 + -20y + 27 = 0

Reorder the terms:
27 + -20y + y2 = 0

Solving
27 + -20y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + -20y + -27 + y2 = 0 + -27

Reorder the terms:
27 + -27 + -20y + y2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -20y + y2 = 0 + -27
-20y + y2 = 0 + -27

Combine like terms: 0 + -27 = -27
-20y + y2 = -27

The y term is -20y.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20y + 100 + y2 = -27 + 100

Reorder the terms:
100 + -20y + y2 = -27 + 100

Combine like terms: -27 + 100 = 73
100 + -20y + y2 = 73

Factor a perfect square on the left side:
(y + -10)(y + -10) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(y + -10) equal to 8.544003745 and -8.544003745.

Subproblem 1

y + -10 = 8.544003745 Simplifying y + -10 = 8.544003745 Reorder the terms: -10 + y = 8.544003745 Solving -10 + y = 8.544003745 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + y = 8.544003745 + 10 Combine like terms: -10 + 10 = 0 0 + y = 8.544003745 + 10 y = 8.544003745 + 10 Combine like terms: 8.544003745 + 10 = 18.544003745 y = 18.544003745 Simplifying y = 18.544003745

Subproblem 2

y + -10 = -8.544003745 Simplifying y + -10 = -8.544003745 Reorder the terms: -10 + y = -8.544003745 Solving -10 + y = -8.544003745 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + y = -8.544003745 + 10 Combine like terms: -10 + 10 = 0 0 + y = -8.544003745 + 10 y = -8.544003745 + 10 Combine like terms: -8.544003745 + 10 = 1.455996255 y = 1.455996255 Simplifying y = 1.455996255

Solution

The solution to the problem is based on the solutions from the subproblems. y = {18.544003745, 1.455996255}

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