Correct answers to these two problems, you!

1) x = -5 ± 4i

2) x = , -

Step-by-step explanation:

On the first one, you lost track of your fraction when you got to the part that's circled. The whole thing should be over 2, not just the -64

you should've had:

x = (-10 ± √(-64)) / 2

then simplify the √(-64):

x = (-10 ± 8i) / 2

x = -5 ± 4i

On the second one, I would've probably done it another way, but ill show you this way

24x² - 42x - 45 = 0

factor out the 3 as you did:

3(8x² - 14x - 15)

here you cant factor the way you did, because a ≠ 1.

when you have ax² + bx + c, you need to split b into 2 terms that multiply to ac and add to b

adds to -14 and multiplies to -120:

6 and -20

split b:

3(8x² + 6x - 20x - 15) = 0

factor by grouping:

3(2x(4x+3) - 5(4x + 3)) = 0

3(2x - 5)(4x + 3) = 0

use the zero product property to solve for x:

2x - 5 = 0

x =

4x + 3 = 0

x = -

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

c is the answer

step-by-step explanation: