y*y+12y=55

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Solution for y*y+12y=55 equation:


Simplifying
y * y + 12y = 55

Multiply y * y
y2 + 12y = 55

Reorder the terms:
12y + y2 = 55

Solving
12y + y2 = 55

Solving for variable 'y'.

Reorder the terms:
-55 + 12y + y2 = 55 + -55

Combine like terms: 55 + -55 = 0
-55 + 12y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '55' to each side of the equation.
-55 + 12y + 55 + y2 = 0 + 55

Reorder the terms:
-55 + 55 + 12y + y2 = 0 + 55

Combine like terms: -55 + 55 = 0
0 + 12y + y2 = 0 + 55
12y + y2 = 0 + 55

Combine like terms: 0 + 55 = 55
12y + y2 = 55

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 = 55 + 36

Reorder the terms:
36 + 12y + y2 = 55 + 36

Combine like terms: 55 + 36 = 91
36 + 12y + y2 = 91

Factor a perfect square on the left side:
(y + 6)(y + 6) = 91

Calculate the square root of the right side: 9.539392014

Break this problem into two subproblems by setting 
(y + 6) equal to 9.539392014 and -9.539392014.

Subproblem 1

y + 6 = 9.539392014 Simplifying y + 6 = 9.539392014 Reorder the terms: 6 + y = 9.539392014 Solving 6 + y = 9.539392014 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 = 9.539392014 + -6 Combine like terms: 6 + -6 = 0 0 + y = 9.539392014 + -6 y = 9.539392014 + -6 Combine like terms: 9.539392014 + -6 = 3.539392014 y = 3.539392014 Simplifying y = 3.539392014

Subproblem 2

y + 6 = -9.539392014 Simplifying y + 6 = -9.539392014 Reorder the terms: 6 + y = -9.539392014 Solving 6 + y = -9.539392014 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 = -9.539392014 + -6 Combine like terms: 6 + -6 = 0 0 + y = -9.539392014 + -6 y = -9.539392014 + -6 Combine like terms: -9.539392014 + -6 = -15.539392014 y = -15.539392014 Simplifying y = -15.539392014

Solution

The solution to the problem is based on the solutions from the subproblems. y = {3.539392014, -15.539392014}

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