Question

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

Answer 1

Answer:

Joanne’s solution is incorrect

The correct solution in the procedure

Step-by-step 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 $x=-1$