PSAT Math Multiple-Choice Question 665: Answer and Explanation

Question: 665

What is/are the solution(s) to the following equation?

• A.
• B.
• C.
• D. No solutions

Correct Answer: A

Explanation:

(A) Get rid of the square root by squaring both sides. Squaring the right side simply gets rid of the square root, but be careful to FOIL the left side:

a² + 8a + 16 = a² - 2

Subtract a² from both sides:

8a + 16 = -2

Next, subtract 16 from both sides:

8a = -18

Solve for a by dividing by 8:

This is choice (A).

Note that squaring equations can lead to extraneous answers. In this case, we don't get any extraneous solutions. However, you should get in the habit of checking your solutions by plugging them back into the original equation to ensure that your solution is truly a solution to the original.