PSAT Math Multiple-Choice Question 612: Answer and Explanation

Question: 612

What is the negative solution to the following equation, rounded to one decimal place?

• A. 1.5
• B. -0.8
• C. -0.6
• D. -1.5

Correct Answer: B

Explanation:

(B) First, we need to get the x out of the denominator by multiplying both sides of the ­equation by x:

We have two x²-terms to combine. So we need a common denominator, which is 3:

This is a quadratic equation since the highest degree of the terms is 2. We bring all terms to the same side so that we can eventually use the quadratic formula:

Recall the quadratic formula for a quadratic equation of the form ax² + bx + c:

Filling in our values for a, b, and c gives:

So or .

We're looking only for the negative value of x, so we only care about the second value. This second value can also be expressed as -0.8077. Rounded to one decimal place, we get choice (B).