40+4y=y^2+4

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Solution for 40+4y=y^2+4 equation:


Simplifying
40 + 4y = y2 + 4

Reorder the terms:
40 + 4y = 4 + y2

Solving
40 + 4y = 4 + y2

Solving for variable 'y'.

Reorder the terms:
40 + -4 + 4y + -1y2 = 4 + y2 + -4 + -1y2

Combine like terms: 40 + -4 = 36
36 + 4y + -1y2 = 4 + y2 + -4 + -1y2

Reorder the terms:
36 + 4y + -1y2 = 4 + -4 + y2 + -1y2

Combine like terms: 4 + -4 = 0
36 + 4y + -1y2 = 0 + y2 + -1y2
36 + 4y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
36 + 4y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-36 + -4y + y2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -4y + 36 + y2 = 0 + 36

Reorder the terms:
-36 + 36 + -4y + y2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -4y + y2 = 0 + 36
-4y + y2 = 0 + 36

Combine like terms: 0 + 36 = 36
-4y + y2 = 36

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4y + 4 + y2 = 36 + 4

Reorder the terms:
4 + -4y + y2 = 36 + 4

Combine like terms: 36 + 4 = 40
4 + -4y + y2 = 40

Factor a perfect square on the left side:
(y + -2)(y + -2) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(y + -2) equal to 6.32455532 and -6.32455532.

Subproblem 1

y + -2 = 6.32455532 Simplifying y + -2 = 6.32455532 Reorder the terms: -2 + y = 6.32455532 Solving -2 + y = 6.32455532 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 6.32455532 + 2 Combine like terms: -2 + 2 = 0 0 + y = 6.32455532 + 2 y = 6.32455532 + 2 Combine like terms: 6.32455532 + 2 = 8.32455532 y = 8.32455532 Simplifying y = 8.32455532

Subproblem 2

y + -2 = -6.32455532 Simplifying y + -2 = -6.32455532 Reorder the terms: -2 + y = -6.32455532 Solving -2 + y = -6.32455532 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -6.32455532 + 2 Combine like terms: -2 + 2 = 0 0 + y = -6.32455532 + 2 y = -6.32455532 + 2 Combine like terms: -6.32455532 + 2 = -4.32455532 y = -4.32455532 Simplifying y = -4.32455532

Solution

The solution to the problem is based on the solutions from the subproblems. y = {8.32455532, -4.32455532}

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