y^2-2y=21

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


Simplifying
y2 + -2y = 21

Reorder the terms:
-2y + y2 = 21

Solving
-2y + y2 = 21

Solving for variable 'y'.

Reorder the terms:
-21 + -2y + y2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + -2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + -2y + 21 + y2 = 0 + 21

Reorder the terms:
-21 + 21 + -2y + y2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -2y + y2 = 0 + 21
-2y + y2 = 0 + 21

Combine like terms: 0 + 21 = 21
-2y + y2 = 21

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = 21 + 1

Reorder the terms:
1 + -2y + y2 = 21 + 1

Combine like terms: 21 + 1 = 22
1 + -2y + y2 = 22

Factor a perfect square on the left side:
(y + -1)(y + -1) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(y + -1) equal to 4.69041576 and -4.69041576.

Subproblem 1

y + -1 = 4.69041576 Simplifying y + -1 = 4.69041576 Reorder the terms: -1 + y = 4.69041576 Solving -1 + y = 4.69041576 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 4.69041576 + 1 Combine like terms: -1 + 1 = 0 0 + y = 4.69041576 + 1 y = 4.69041576 + 1 Combine like terms: 4.69041576 + 1 = 5.69041576 y = 5.69041576 Simplifying y = 5.69041576

Subproblem 2

y + -1 = -4.69041576 Simplifying y + -1 = -4.69041576 Reorder the terms: -1 + y = -4.69041576 Solving -1 + y = -4.69041576 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -4.69041576 + 1 Combine like terms: -1 + 1 = 0 0 + y = -4.69041576 + 1 y = -4.69041576 + 1 Combine like terms: -4.69041576 + 1 = -3.69041576 y = -3.69041576 Simplifying y = -3.69041576

Solution

The solution to the problem is based on the solutions from the subproblems. y = {5.69041576, -3.69041576}

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