Question

Given x^2 - 6x + 9 = 0 and x + k = 1, find the value of k

-
A. 3
B. -4
C. -2
D.1

Answer 1

C: k=-2

Explanation:

Eq 1:
`x^(2)`-6x+9=0

Eq 2: x+k=1

Solve Eq 2 for x:

x=1-k

Sub x into Eq 1:

`(1-k)^(2)`-6(1-k)+9=0

Solve for k:

`k^(2)`-2k+1-6+6k+9=0

`k^(2)`+4k+4=0

Factor:

`(k+2)^(2)`=0

Square root both sides:

k+2=0

k=-2