y^2=4y+9

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Solution for y^2=4y+9 equation:


Simplifying
y2 = 4y + 9

Reorder the terms:
y2 = 9 + 4y

Solving
y2 = 9 + 4y

Solving for variable 'y'.

Reorder the terms:
-9 + -4y + y2 = 9 + 4y + -9 + -4y

Reorder the terms:
-9 + -4y + y2 = 9 + -9 + 4y + -4y

Combine like terms: 9 + -9 = 0
-9 + -4y + y2 = 0 + 4y + -4y
-9 + -4y + y2 = 4y + -4y

Combine like terms: 4y + -4y = 0
-9 + -4y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -4y + 9 + y2 = 0 + 9

Reorder the terms:
-9 + 9 + -4y + y2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -4y + y2 = 0 + 9
-4y + y2 = 0 + 9

Combine like terms: 0 + 9 = 9
-4y + y2 = 9

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 = 9 + 4

Reorder the terms:
4 + -4y + y2 = 9 + 4

Combine like terms: 9 + 4 = 13
4 + -4y + y2 = 13

Factor a perfect square on the left side:
(y + -2)(y + -2) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(y + -2) equal to 3.605551275 and -3.605551275.

Subproblem 1

y + -2 = 3.605551275 Simplifying y + -2 = 3.605551275 Reorder the terms: -2 + y = 3.605551275 Solving -2 + y = 3.605551275 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 = 3.605551275 + 2 Combine like terms: -2 + 2 = 0 0 + y = 3.605551275 + 2 y = 3.605551275 + 2 Combine like terms: 3.605551275 + 2 = 5.605551275 y = 5.605551275 Simplifying y = 5.605551275

Subproblem 2

y + -2 = -3.605551275 Simplifying y + -2 = -3.605551275 Reorder the terms: -2 + y = -3.605551275 Solving -2 + y = -3.605551275 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 = -3.605551275 + 2 Combine like terms: -2 + 2 = 0 0 + y = -3.605551275 + 2 y = -3.605551275 + 2 Combine like terms: -3.605551275 + 2 = -1.605551275 y = -1.605551275 Simplifying y = -1.605551275

Solution

The solution to the problem is based on the solutions from the subproblems. y = {5.605551275, -1.605551275}

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