Completing the square method allows you to solve any quadratic equation. For each of the following determine what number completes the square.

I cannot find my notes on completing the square, can someone please help with these two problems?
1. x^2+8x
2. y^2+10y

i don't know ha!

I don't think that's very nice if you don't know don't post an answer unless it helps people! Can someone that DOES know please help me? Thank you.

1. x(x+8)

2. y(y+10)

Of course! I'd be happy to help you with these problems using the completing the square method.

To complete the square for a quadratic equation of the form x^2 + bx, y^2 + by, you need to take half of the coefficient of the variable (b), square it, and add it to the equation. This will allow you to create a perfect square trinomial, which can then be factored and solved.

Now let's solve the two problems you mentioned step by step:

1. x^2 + 8x:
To complete the square for this equation, we need to find the number that will make it a perfect square trinomial. We take half of the coefficient of x, which is 8, and square it to get 16.
Next, we add 16 to the equation:
x^2 + 8x + 16
Now, we can factor the equation:
(x + 4)(x + 4)
Simplifying the factored form, we get:
(x + 4)^2
So, the number that completes the square for x^2 + 8x is 16, and the factored form is (x + 4)^2.

2. y^2 + 10y:
Similar to the previous problem, we need to find the number that makes this equation a perfect square trinomial. Taking half of the coefficient of y, which is 10, and squaring it gives us 25.
Adding 25 to the equation, we have:
y^2 + 10y + 25
Factoring the equation, we get:
(y + 5)(y + 5)
Simplifying the factored form, we have:
(y + 5)^2
Therefore, for y^2 + 10y, the number that completes the square is 25, and the factored form is (y + 5)^2.

I hope this explanation helps you understand how to complete the square for quadratic equations. Let me know if you have any further questions!