y^2-12y=-21

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Solution for y^2-12y=-21 equation:


Simplifying
y2 + -12y = -21

Reorder the terms:
-12y + y2 = -21

Solving
-12y + y2 = -21

Solving for variable 'y'.

Reorder the terms:
21 + -12y + y2 = -21 + 21

Combine like terms: -21 + 21 = 0
21 + -12y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + -12y + -21 + y2 = 0 + -21

Reorder the terms:
21 + -21 + -12y + y2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -12y + y2 = 0 + -21
-12y + y2 = 0 + -21

Combine like terms: 0 + -21 = -21
-12y + y2 = -21

The y term is -12y.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12y + 36 + y2 = -21 + 36

Reorder the terms:
36 + -12y + y2 = -21 + 36

Combine like terms: -21 + 36 = 15
36 + -12y + y2 = 15

Factor a perfect square on the left side:
(y + -6)(y + -6) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(y + -6) equal to 3.872983346 and -3.872983346.

Subproblem 1

y + -6 = 3.872983346 Simplifying y + -6 = 3.872983346 Reorder the terms: -6 + y = 3.872983346 Solving -6 + y = 3.872983346 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = 3.872983346 + 6 Combine like terms: -6 + 6 = 0 0 + y = 3.872983346 + 6 y = 3.872983346 + 6 Combine like terms: 3.872983346 + 6 = 9.872983346 y = 9.872983346 Simplifying y = 9.872983346

Subproblem 2

y + -6 = -3.872983346 Simplifying y + -6 = -3.872983346 Reorder the terms: -6 + y = -3.872983346 Solving -6 + y = -3.872983346 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = -3.872983346 + 6 Combine like terms: -6 + 6 = 0 0 + y = -3.872983346 + 6 y = -3.872983346 + 6 Combine like terms: -3.872983346 + 6 = 2.127016654 y = 2.127016654 Simplifying y = 2.127016654

Solution

The solution to the problem is based on the solutions from the subproblems. y = {9.872983346, 2.127016654}

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