y^2-12y+23=0

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Solution for y^2-12y+23=0 equation:


Simplifying
y2 + -12y + 23 = 0

Reorder the terms:
23 + -12y + y2 = 0

Solving
23 + -12y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-23' to each side of the equation.
23 + -12y + -23 + y2 = 0 + -23

Reorder the terms:
23 + -23 + -12y + y2 = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -12y + y2 = 0 + -23
-12y + y2 = 0 + -23

Combine like terms: 0 + -23 = -23
-12y + y2 = -23

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 = -23 + 36

Reorder the terms:
36 + -12y + y2 = -23 + 36

Combine like terms: -23 + 36 = 13
36 + -12y + y2 = 13

Factor a perfect square on the left side:
(y + -6)(y + -6) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(y + -6) equal to 3.605551275 and -3.605551275.

Subproblem 1

y + -6 = 3.605551275 Simplifying y + -6 = 3.605551275 Reorder the terms: -6 + y = 3.605551275 Solving -6 + y = 3.605551275 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 = 3.605551275 + 6 Combine like terms: -6 + 6 = 0 0 + y = 3.605551275 + 6 y = 3.605551275 + 6 Combine like terms: 3.605551275 + 6 = 9.605551275 y = 9.605551275 Simplifying y = 9.605551275

Subproblem 2

y + -6 = -3.605551275 Simplifying y + -6 = -3.605551275 Reorder the terms: -6 + y = -3.605551275 Solving -6 + y = -3.605551275 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 = -3.605551275 + 6 Combine like terms: -6 + 6 = 0 0 + y = -3.605551275 + 6 y = -3.605551275 + 6 Combine like terms: -3.605551275 + 6 = 2.394448725 y = 2.394448725 Simplifying y = 2.394448725

Solution

The solution to the problem is based on the solutions from the subproblems. y = {9.605551275, 2.394448725}

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