y^2+16y=5

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Solution for y^2+16y=5 equation:


Simplifying
y2 + 16y = 5

Reorder the terms:
16y + y2 = 5

Solving
16y + y2 = 5

Solving for variable 'y'.

Reorder the terms:
-5 + 16y + y2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 16y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 16y + 5 + y2 = 0 + 5

Reorder the terms:
-5 + 5 + 16y + y2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 16y + y2 = 0 + 5
16y + y2 = 0 + 5

Combine like terms: 0 + 5 = 5
16y + y2 = 5

The y term is 16y.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16y + 64 + y2 = 5 + 64

Reorder the terms:
64 + 16y + y2 = 5 + 64

Combine like terms: 5 + 64 = 69
64 + 16y + y2 = 69

Factor a perfect square on the left side:
(y + 8)(y + 8) = 69

Calculate the square root of the right side: 8.306623863

Break this problem into two subproblems by setting 
(y + 8) equal to 8.306623863 and -8.306623863.

Subproblem 1

y + 8 = 8.306623863 Simplifying y + 8 = 8.306623863 Reorder the terms: 8 + y = 8.306623863 Solving 8 + y = 8.306623863 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + y = 8.306623863 + -8 Combine like terms: 8 + -8 = 0 0 + y = 8.306623863 + -8 y = 8.306623863 + -8 Combine like terms: 8.306623863 + -8 = 0.306623863 y = 0.306623863 Simplifying y = 0.306623863

Subproblem 2

y + 8 = -8.306623863 Simplifying y + 8 = -8.306623863 Reorder the terms: 8 + y = -8.306623863 Solving 8 + y = -8.306623863 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + y = -8.306623863 + -8 Combine like terms: 8 + -8 = 0 0 + y = -8.306623863 + -8 y = -8.306623863 + -8 Combine like terms: -8.306623863 + -8 = -16.306623863 y = -16.306623863 Simplifying y = -16.306623863

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.306623863, -16.306623863}

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