# How do you solve the quadratic equation by completing the square: #y^2 + 16y = 2#?

You apply the following formula to finish the square:

a has to equal 1.

The square when finished is:

Now, the x in the general formula is represented by the y in your function:

now resolve c:

now finish the square:

Now resolve:

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To solve the quadratic equation by completing the square, follow these steps:

- Rewrite the equation in the form ( y^2 + 16y + \text{(some number)} = 2 + \text{(same number)} ) by adding and subtracting the square of half of the coefficient of ( y ).
- Factor the trinomial as a perfect square.
- Solve for ( y ) by taking the square root of both sides.
- Simplify the solution.

Applying these steps to the equation ( y^2 + 16y = 2 ), we get:

- Add and subtract ( (16/2)^2 = 64 ): ( y^2 + 16y + 64 - 64 = 2 )
- Factor the trinomial as a perfect square: ( (y + 8)^2 - 64 = 2 )
- Solve for ( y ) by taking the square root of both sides: ( y + 8 = \pm \sqrt{66} )
- Simplify the solution: ( y = -8 \pm \sqrt{66} )

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