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

x= 18 or x=11

Step-by-step explanation:

Given the equation as

(x-8)² -13(x-8)+30=01

Let x-8 to be substituted by u

So x-8=u2

Use equation 2 in equation 1

(u)² -13(u) +30 =0

u²-13u+30=0factorize

u²-3u-10u+30=0

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

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

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.