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

Take half of the coefficent of the x term, square it.

1) half of eight, squared : 16
2) half of ten, squared: 25

Take half of the coefficent of the x term, square it.

1) half of eight, squared : 16
2) half of ten, squared: 25

To complete the square for each of the given quadratic equations, we will use the numbers obtained above.

1. x^2 + 8x:
Now, we add and subtract the square value obtained, 16, inside the equation:
x^2 + 8x + 16 - 16

2. y^2 + 10y:
Similar to the previous equation, we add and subtract the square of half of the coefficient of the y term, 25, inside the equation:
y^2 + 10y + 25 - 25

So, the expressions after completing the square will be:
1. x^2 + 8x + 16 - 16
2. y^2 + 10y + 25 - 25

Simplified versions:
1. (x + 4)^2 - 16
2. (y + 5)^2 - 25

In completing the square, we have transformed the original quadratic equations into perfect square trinomials, which can be easily solved.

To complete the square, you need to find a number that, when added to the quadratic expression, creates a perfect square trinomial. This number can be found by taking half of the coefficient of the linear term (the x or y term in this case) and squaring it.

For the first problem, the coefficient of the x term is 8. Taking half of 8 gives you 4. Squaring 4 gives you 16. So to complete the square for the expression x^2 + 8x, you can add 16 to it.

For the second problem, the coefficient of the y term is 10. Half of 10 is 5, and squaring 5 gives you 25. So to complete the square for the expression y^2 + 10y, you can add 25 to it.

Therefore, the numbers that complete the square for the given expressions are:
1. For x^2 + 8x, the number that completes the square is 16.
2. For y^2 + 10y, the number that completes the square is 25.