Question

What are the solutions of the quadratic equation (x – 8)2 – 13(x – 8) + 30 = 0? Use u substitution to solve.

Answer 1

It is 11 and 18 positive not negative numbers

Explanation:

Answer 2

it is a quadratic
where x-8 is the squared term
do
x-8=u

u^2-13u+30=0

solve
u=
`(-b+/- √(b^2-4ac) )/(2a)`
u=
`(-(-13)+/- √((-13)^2-4(1)(30)) )/(2(1))`
u=
`(13+/- √(169-120) )/(2)`
u=
`(13+/- √(49) )/(2)`
u=
`(13+/- 7 )/(2)`
u=
`\frac{20} }{2}` or u=
`(6 )/(2)`
u=10 or 3

10=x-8 or 3=x-8
18=x or 11=x

x=11 and/or 18