Cedric completed the square for the quadratic expression 5x^2−40x+15 in order to determine the minimum value of the expression, as shown.
Step 1: 5(x^2−8x+3)
Step 2: 5(x^2−8x+16−16+3)
Step 3: 5((x+4)^2−16+3)
Step 4: 5((x+4)^2−13)
Step 5: 5(x+4)^2−65
What mistake, if any, did Cedric make?

Step 3 is not correct (should be , not

Step-by-step explanation:

The expression that we have to simplify is:

We proceed step-by-step, in order to find the mistake did by Cedric:

1) First, we factorize the 5 outside:

--> this step is correct

2) We add +16 and -16 inside the brackets:

--> this step is correct

3) We rewrite the term as the square of a bynomial, which is , so the expression becomes

--> we notice that this step is wrong: in fact, Cedric wrote , which is not correct.

4) Now we continue: we rewrite -16+3 as -13,

5) Finally, we multiply the 5 by the terms in the bracket:

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square

9

step-by-step explanation: