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.