y^2-13y+30=12

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Solution for y^2-13y+30=12 equation:


Simplifying
y2 + -13y + 30 = 12

Reorder the terms:
30 + -13y + y2 = 12

Solving
30 + -13y + y2 = 12

Solving for variable 'y'.

Reorder the terms:
30 + -12 + -13y + y2 = 12 + -12

Combine like terms: 30 + -12 = 18
18 + -13y + y2 = 12 + -12

Combine like terms: 12 + -12 = 0
18 + -13y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -13y + -18 + y2 = 0 + -18

Reorder the terms:
18 + -18 + -13y + y2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -13y + y2 = 0 + -18
-13y + y2 = 0 + -18

Combine like terms: 0 + -18 = -18
-13y + y2 = -18

The y term is -13y.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13y + 42.25 + y2 = -18 + 42.25

Reorder the terms:
42.25 + -13y + y2 = -18 + 42.25

Combine like terms: -18 + 42.25 = 24.25
42.25 + -13y + y2 = 24.25

Factor a perfect square on the left side:
(y + -6.5)(y + -6.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(y + -6.5) equal to 4.924428901 and -4.924428901.

Subproblem 1

y + -6.5 = 4.924428901 Simplifying y + -6.5 = 4.924428901 Reorder the terms: -6.5 + y = 4.924428901 Solving -6.5 + y = 4.924428901 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + y = 4.924428901 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + y = 4.924428901 + 6.5 y = 4.924428901 + 6.5 Combine like terms: 4.924428901 + 6.5 = 11.424428901 y = 11.424428901 Simplifying y = 11.424428901

Subproblem 2

y + -6.5 = -4.924428901 Simplifying y + -6.5 = -4.924428901 Reorder the terms: -6.5 + y = -4.924428901 Solving -6.5 + y = -4.924428901 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + y = -4.924428901 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + y = -4.924428901 + 6.5 y = -4.924428901 + 6.5 Combine like terms: -4.924428901 + 6.5 = 1.575571099 y = 1.575571099 Simplifying y = 1.575571099

Solution

The solution to the problem is based on the solutions from the subproblems. y = {11.424428901, 1.575571099}

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