# SAT Math Multiple Choice Question 770: Answer and Explanation

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**Question: 770**

**5.** If , which of the following expressions gives both possible values of *x*, in terms of *p*?

- A.
- B.
- C.
- D.

**Correct Answer:** C

**Explanation:**

**C**

**Algebra (rewriting expressions) MEDIUM-HARD**

Original equation:

Multiply by 2*p* (the common denominator):

*p*(*x*^{2} + 1) + 2*x* = 2*p*

Distribute:

*px*^{2} + *p* + 2*x* = 2*p*

Subtract 2*p* and write in descending powers of *x*:

*px*^{2} + 2*x* - *p* = 0

Put into quadratic formula with *a* = *p*, *b* = 2, and *c* = -*p*: