Question

solve the following quadratic equations by completing the square method in 1) x^2+8x+9=0​

Answer 1

Answer:

Step-by-step explanation:

given that

x^2+8x+9

we know in completing the square method,

1) we take coefficient of x and divide it by 2,

2) then square it and add/subtract.

Let's follow these two steps

1) coefficient of x is 8, and dividing it by 2 = 4

2) square of 4 is 16 and let's add/subtract this 16

x^2+8x+16-16+9

we find first three terms make it a perfect square

then

(x^2+8x+16)-7

we can further write it as

(x+4)^2 - 7

Now remember the difference of square rule

(a^2 - b^2) = (a+b) (a-b)

so equation we obtained can be written as

(x+4)^2 - (√7)^2

= (x+4-√7)(x+4-√7)

these are the factors of the quadratic equation