Find the roots of the quadratic equation x2 – 8x = 9 by completing the square. show your work.

The answer is -1 or 9

The quadratic equation is ax² + bx + c  = 0. But, by completing the square we turn it into: a(x + d)² + e = 0, where:

d = b/2a

e = c - b²/4a

Our quadratic equation is x² - 8x = 9, which is after rearrangement:

x² - 8x - 9 = 0

So, a = 1, b = -8, c = -9

Let's first calculate d and e:

d = b/2a = -8/(2 * 1) = -8/2 = -4

e = c - b²/4a = -9 - (-8)²/(4 * 1) = -9 - 64/4 = -9 - 16 = -25

By completing the square we have:

a(x + d)² + e = 0

1(x + (-4))² + (-25) = 0

(x - 4)² - 25 = 0

(x - 4)² = 25

⇒ x - 4 = √25

Since √25 can be either -5  or +5 , then:

x - 4 = -5             or           x - 4 = 5

x = -5 + 4            or           x = 5 + 4

x = -1                   or           x = 9

Step-by-step explanation:

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!