Solve the following quadratic equation for x by completing the square and solve x^2-8x=-65

x= 4-7i  x= 4+ 7i

Step-by-step explanation:

step 1 : make equation = 0

- 8x + 65 = 0

step 2 : solve for x [ using the quadratic equation]

ie :     x = -b ± / 2a

so it will look like this

x= -(-8) ± /2(1)

when you simplify you wont be able to root the -196 so you will have to separate the roots

x = 8 ±( )( ) / 2

now there is a rule for negative roots whereby   is equivalent to i so now you will change into i

Simplify

which will give you 14

now place all the new values into the formula

8 ± 14i /2

you can then further simplify to  

4 ± 7i

step 3 : separate

this will give you the final answer of

x= 4 + 7i   x= 4- 7i

n

step-by-step explanation:

30 miles

step-by-step explanation:

we know that 60 seconds equals 1 minute and 60 minutes 1 hour

44 ft       60 sec     60 min     158400   ft

  *   *   =

1 sec       1 min       1 hour         hour

we know that there are 5280 ft per mile

158400   ft       1 mile         30 miles

  *   =

1   hour               5280 ft     1 hour

so in 1 hour   it can travel 30 miles