Solve the polynomial by completing the square. Show all steps of your work. x^2 - 11x + 24 = 0

Question

Solve the polynomial by completing the square. Show all steps of your work.


`x^2 - 11x + 24 = 0`

Answer 1

Given equation:
x
2
+11x+24=0
Adding (
2
11
​
)
2
on both side, we get
x
2
+11x+
4
121
​
+24=
4
121
​

⇒(x+
2
11
​
)
2
=
4
121
​
−24=
4
25
​

⇒x+
2
11
​
=±
2
5
​

⇒x=±
2
5
​
−
2
11
​

⇒x=−8 or x=−3

Answer 2

Find the common factors that multiply to get 24 and add to get -11 (-8,-3)
Set them equal to 0
-8=0 -3=0 switch the signs
{3,8}