Question

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

Answer 1

x= 18 or x=11

Explanation:

Given the equation as

(x-8)² -13(x-8)+30=0------------------------1

Let x-8 to be substituted by u

So x-8=u--------------------------------------2

Use equation 2 in equation 1

(u)² -13(u) +30 =0

u²-13u+30=0------------------factorize

u²-3u-10u+30=0

u(u-3)-10(u-3)=0

(u-10) (u-3) =0---------------find value of u

u-10=0

u=10 or

u-3=0

u=3

Use values of u in equation 2

when u=10

but u=x-8

hence 10=x-8

x=10+8=18

or

when u=3

hence 3=x-8

x=3+8=11

x= 18 or x=11