Question

This is Mrs. Galicia’s solution for the equation. Is Mrs. Galicia’s solution correct? Explain in complete sentences also, what are the correct solutions.

Answer 1

Given:

Given that Mrs. Galicia’s solution for the equation.

We need to determine whether Mrs. Galicia’s solution is correct or not.

Also, we need to determine the correct solutions.

Mrs. Galicia’s solution:

Step 4: $(x-4)^2=25$

Step 5: $x-4=25$

After step 4, Mrs. Galicia’s did not take square root on both sides to determine the value of x.

Thus, Mrs. Galicia’s made in mistake in step 5, by solving the equation without taking square root on both sides.

Hence, Mrs. Galicia’s solution is wrong.

Correct solutions:

The equation is $x^{2} -8x-9=0$

Solving, we get;

$x^2-8x=9$

Completing the square, we have;

$x^2-8x+16=9+16$

      $(x-4)^2=25$

Taking square root on both sides, we get;

$x-4=\pm 5$

Thus, the values of x are given by

$x-4=5$ and $x-4=-5$

     $x=9$ and       $x=-1$

Thus, the correct solutions are x = 9 and x = -1