y^2-20y-1=0

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Solution for y^2-20y-1=0 equation:


Simplifying
y2 + -20y + -1 = 0

Reorder the terms:
-1 + -20y + y2 = 0

Solving
-1 + -20y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -20y + 1 + y2 = 0 + 1

Reorder the terms:
-1 + 1 + -20y + y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -20y + y2 = 0 + 1
-20y + y2 = 0 + 1

Combine like terms: 0 + 1 = 1
-20y + y2 = 1

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 = 1 + 100

Reorder the terms:
100 + -20y + y2 = 1 + 100

Combine like terms: 1 + 100 = 101
100 + -20y + y2 = 101

Factor a perfect square on the left side:
(y + -10)(y + -10) = 101

Calculate the square root of the right side: 10.049875621

Break this problem into two subproblems by setting 
(y + -10) equal to 10.049875621 and -10.049875621.

Subproblem 1

y + -10 = 10.049875621 Simplifying y + -10 = 10.049875621 Reorder the terms: -10 + y = 10.049875621 Solving -10 + y = 10.049875621 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 = 10.049875621 + 10 Combine like terms: -10 + 10 = 0 0 + y = 10.049875621 + 10 y = 10.049875621 + 10 Combine like terms: 10.049875621 + 10 = 20.049875621 y = 20.049875621 Simplifying y = 20.049875621

Subproblem 2

y + -10 = -10.049875621 Simplifying y + -10 = -10.049875621 Reorder the terms: -10 + y = -10.049875621 Solving -10 + y = -10.049875621 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 = -10.049875621 + 10 Combine like terms: -10 + 10 = 0 0 + y = -10.049875621 + 10 y = -10.049875621 + 10 Combine like terms: -10.049875621 + 10 = -0.049875621 y = -0.049875621 Simplifying y = -0.049875621

Solution

The solution to the problem is based on the solutions from the subproblems. y = {20.049875621, -0.049875621}

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