Answer:
1) x = -5 ± 4i
2) x = [tex]\frac{5}{2}[/tex], - [tex]\frac{3}{4}[/tex]
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 = [tex]\frac{5}{2}[/tex]
4x + 3 = 0
x = - [tex]\frac{3}{4}[/tex]
