Question

This is Joanne’s solution for the equation x2 – 10x – 11 = 0

x2 – 10x – 11 = 0
x2 – 10x = 11
x2 – 10x + 25 = 11 + 25
(x – 5)2 = 36
x – 5 = 36 or x – 5= -25
x = 41 x = -20
The solution is x = 41 or x = -20

a) Is Joanne’s solution correct? Why or Why not?
b) If Joanne’s solution is incorrect, circle and explain her error and show how to do this problem correctly using the complete the square method that was used above.

Answer:

Answer 1

Joanne’s solution is incorrect

The correct solution in the procedure

Explanation:

we have

`x^(2)-10x-11=0`

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`x^(2)-10x=11`

Complete the square. Remember to balance the equation by adding the same constants to each side

`x^(2)-10x+25=11+25`

`x^(2)-10x+25=36`

Rewrite as perfect squares

`(x-5)^(2)=36`

So far Joanne's procedure was correct, then she was wrong to take the square root on both sides.

take square root both sides

`(x-5)=(+/-)6`

`x=5(+/-)6`

`x1=5(+)6=11`

`x2=5(-)6=-1`

The solution is
`x=11` or
`x=-1`