# SAT Math Multiple Choice Question 717: Answer and Explanation

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**Question: 717**

**12.** 3*x*^{2} = 4*x* + *c*

In the equation above, *c* is a constant. If *x* = -1 is a solution of this equation, what other value of *x* satisfies the equation?

- A.
- B.
- C.
- D. 7

**Correct Answer:** C

**Explanation:**

**C**

**Advanced Mathematics (quadratics) HARD**

We can find the value of *c* by just substituting *x* = -1 into the equation.

Given equation:

3*x*^{2} = 4*x* + *c*

Substitute *x* = -1:

3(-1)^{2} = 4(-1) + *c*

Simplify:

3 = -4 + *c*

Add 4:

7 = *c*

Therefore, the equation is:

3*x*^{2} = 4*x* + 7

Subtract 4*x* and 7:

3*x*^{2} - 4*x* - 7 = 0

Factor using Sum-Product Method:

(*x* + 1)(3*x* - 7) = 0

(Notice that the factor (*x* + 1) corresponds to the fact that *x* = -1 is a solution to the quadratic.)

Use Zero Product Property to find other solution:

3*x* - 7 = 0

Add 7:

3*x* = 7

Divide by 3:

*x* = 7/3