To find the value of [tex]\( k \)[/tex] in the equation [tex]\( x^2 - 3x + k = 2 \)[/tex], let's follow these steps:
1. Start with the given equation:
[tex]\[
x^2 - 3x + k = 2
\][/tex]
2. Rearrange the equation to isolate [tex]\( k \)[/tex]:
[tex]\[
x^2 - 3x + k - 2 = 0
\][/tex]
This can be rewritten as:
[tex]\[
x^2 - 3x + (k - 2) = 0
\][/tex]
3. Solve for [tex]\( k \)[/tex]:
Now, let's assume a particular value of [tex]\( x \)[/tex] to find [tex]\( k \)[/tex].
Given [tex]\( x = 2 \)[/tex]:
Plug [tex]\( x = 2 \)[/tex] into the equation:
[tex]\[
(2)^2 - 3(2) + (k - 2) = 0
\][/tex]
Simplify this equation step-by-step:
[tex]\[
4 - 6 + k - 2 = 0
\][/tex]
Combine like terms:
[tex]\[
4 - 6 - 2 + k = 0
\][/tex]
Simplify further:
[tex]\[
-4 + k = 0
\][/tex]
4. Isolate [tex]\( k \)[/tex]:
Add 4 to both sides of the equation to solve for [tex]\( k \)[/tex]:
[tex]\[
k = 4
\][/tex]
So, the value of [tex]\( k \)[/tex] is:
[tex]\[
k = 4
\][/tex]
