y^2-12y+36=3

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Solution for y^2-12y+36=3 equation:


Simplifying
y2 + -12y + 36 = 3

Reorder the terms:
36 + -12y + y2 = 3

Solving
36 + -12y + y2 = 3

Solving for variable 'y'.

Reorder the terms:
36 + -3 + -12y + y2 = 3 + -3

Combine like terms: 36 + -3 = 33
33 + -12y + y2 = 3 + -3

Combine like terms: 3 + -3 = 0
33 + -12y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-33' to each side of the equation.
33 + -12y + -33 + y2 = 0 + -33

Reorder the terms:
33 + -33 + -12y + y2 = 0 + -33

Combine like terms: 33 + -33 = 0
0 + -12y + y2 = 0 + -33
-12y + y2 = 0 + -33

Combine like terms: 0 + -33 = -33
-12y + y2 = -33

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 = -33 + 36

Reorder the terms:
36 + -12y + y2 = -33 + 36

Combine like terms: -33 + 36 = 3
36 + -12y + y2 = 3

Factor a perfect square on the left side:
(y + -6)(y + -6) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(y + -6) equal to 1.732050808 and -1.732050808.

Subproblem 1

y + -6 = 1.732050808 Simplifying y + -6 = 1.732050808 Reorder the terms: -6 + y = 1.732050808 Solving -6 + y = 1.732050808 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 = 1.732050808 + 6 Combine like terms: -6 + 6 = 0 0 + y = 1.732050808 + 6 y = 1.732050808 + 6 Combine like terms: 1.732050808 + 6 = 7.732050808 y = 7.732050808 Simplifying y = 7.732050808

Subproblem 2

y + -6 = -1.732050808 Simplifying y + -6 = -1.732050808 Reorder the terms: -6 + y = -1.732050808 Solving -6 + y = -1.732050808 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 = -1.732050808 + 6 Combine like terms: -6 + 6 = 0 0 + y = -1.732050808 + 6 y = -1.732050808 + 6 Combine like terms: -1.732050808 + 6 = 4.267949192 y = 4.267949192 Simplifying y = 4.267949192

Solution

The solution to the problem is based on the solutions from the subproblems. y = {7.732050808, 4.267949192}

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