Answer:
no solution
Explanation:
Let's solve your equation step-by-step.
x2−3x+41=0
Step 1: Subtract 41 from both sides.
x2−3x+41−41=0−41
x2−3x=−41
Step 2: The coefficient of -3x is -3. Let b=-3.
Then we need to add (b/2)^2=9/4 to both sides to complete the square.
Add 9/4 to both sides.
x2−3x+
9
4
=−41+
9
4
x2−3x+
9
4
=
−155
4
Step 3: Factor left side.
(x
−3
2
)2=
−155
4
Step 4: Take square root.
x
−3
2
=±√
−155
4
Step 5: Add 3/2 to both sides.
x
−3
2
+
3
2
=
3
2
±√
−155
4
x=
3
2
±√
−155
4
Answer:
No real solutions.