Final answer:
Marla made a mistake in the steps to complete the square for the expression -4x^2 + 83x - 25. She did not correctly calculate the number to add and subtract, resulting in incorrect values and steps. The correct steps would involve using (83/8)^2 instead of 16 when completing the square.
Step-by-step explanation:
To check if Marla used the correct steps to complete the square for the quadratic expression -4x^2 + 83x - 25, let's carefully examine the steps she took:
Original expression: -4x^2 + 83x - 25
Step 1 seems to be an incorrectly copied version of the expression; let's assume Marla started with -4x^2 + 83x - 25.
Step 2: She factored out the coefficient of x^2, which is -4, from the first two terms, obtaining -4(x^2 - (83/4)x) - 25. But Marla incorrectly showed 8x instead of the correct (83/4)x in her steps.
Step 3: To complete the square, we need to take half of the coefficient of x (from x^2 term) and square it. Marla added and then subtracted (8/2)^2 = 16 inside the parenthesis, but it should have been ((83/8)/2)^2. She ended up with -4(x^2 + 16x + 16) + 64 - 25.
Step 4: She simplified the completed square and added together the constants 64 and -25, giving the final expression -4(x + 4)^2 + 39.
Therefore, Marla's steps were incorrect because she didn't correctly calculate the number to add and subtract to complete the square. The correct step to finish completing the square would involve using (83/8)^2 rather than 16 in Step 3.