Question

0=(x-8) (3x-5) show all work

Answer 1

x = 8

`x=1(2)/(3)`

Explanation:

0 = (x - 8)(3x - 5)

(x - 8)(3x - 5) = 0

x(3x - 5) - 8(3x - 5) = 0

3x² - 5x - 8(3x - 5) = 0

3x² - 5x - 24x + 40 = 0

3x² - 29x + 40 = 0

`x=\frac{-b±\sqrt{b^(2)-4ac } }{2a}`

Ignore the A before the ±. It wouldn't let me type it correctly.

3x² - 29x + 40 = 0

a = 3

b = - 29

c = 40

`x=\frac{-(-29)±\sqrt{(-29)^(2)-4((3)(40)) } }{2(3)}`

`x=(-(-29)±√(841-4((3)(40)) ) )/(2(3))`

`x=(29±√(841-480) )/(2(3))`

`x=(29±√(361) )/(2(3))`

`x=(29±19 )/(2(3))`

`x=(29±19 )/(6)`

Two separate equations

`x=(29+19 )/(6)`

`x=(48 )/(6)`

x = 8

`x=(29-19 )/(6)`

`x=(10 )/(6)`

`x=(5 )/(3)`

`x=1(2)/(3)`