y^2+12y=7

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Solution for y^2+12y=7 equation:


Simplifying
y2 + 12y = 7

Reorder the terms:
12y + y2 = 7

Solving
12y + y2 = 7

Solving for variable 'y'.

Reorder the terms:
-7 + 12y + y2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 12y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 12y + 7 + y2 = 0 + 7

Reorder the terms:
-7 + 7 + 12y + y2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 12y + y2 = 0 + 7
12y + y2 = 0 + 7

Combine like terms: 0 + 7 = 7
12y + y2 = 7

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 = 7 + 36

Reorder the terms:
36 + 12y + y2 = 7 + 36

Combine like terms: 7 + 36 = 43
36 + 12y + y2 = 43

Factor a perfect square on the left side:
(y + 6)(y + 6) = 43

Calculate the square root of the right side: 6.557438524

Break this problem into two subproblems by setting 
(y + 6) equal to 6.557438524 and -6.557438524.

Subproblem 1

y + 6 = 6.557438524 Simplifying y + 6 = 6.557438524 Reorder the terms: 6 + y = 6.557438524 Solving 6 + y = 6.557438524 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 = 6.557438524 + -6 Combine like terms: 6 + -6 = 0 0 + y = 6.557438524 + -6 y = 6.557438524 + -6 Combine like terms: 6.557438524 + -6 = 0.557438524 y = 0.557438524 Simplifying y = 0.557438524

Subproblem 2

y + 6 = -6.557438524 Simplifying y + 6 = -6.557438524 Reorder the terms: 6 + y = -6.557438524 Solving 6 + y = -6.557438524 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 = -6.557438524 + -6 Combine like terms: 6 + -6 = 0 0 + y = -6.557438524 + -6 y = -6.557438524 + -6 Combine like terms: -6.557438524 + -6 = -12.557438524 y = -12.557438524 Simplifying y = -12.557438524

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.557438524, -12.557438524}

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