Digital PSAT Math Practice Question 285: Answer and Explanation

Question: 285

Which of the following is a solution to the equation below?

(a + 5)² + 4 = 68

• A. 2
• B. 3
• C. 8
• D. 13

Correct Answer: B

Explanation:

(B) First, you need to FOIL the squared term:

(a + 5)(a + 5) = a² + 10a + 25

Substituting this back into the equation gives you

a² + 10a + 25 + 4 = 68

Bringing everything to the left side of the equation and combining like terms leaves

a² + 10a - 39 = 0

This can be factored to

(a + 13)(a - 3) = 0

Setting each factor equal to 0 gives

a + 13 = 0, so a = - 13

a - 3 = 0, so a = 3

Out of these two choices, only 3 is an option. Therefore, the correct answer is choice (B). Alternatively, you could have used the quadratic formula for the last step.