If x 2 – x = 12, what is one possible value of x?

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Accepted Answer

Combine like terms on one side of the equation and set the expression equal to 0; x 2 – x = 12, x 2 – x – 12 = 0. Factor the quadratic and set each factor equal to 0 to find the solutions for x. To find the factors of a quadratic, begin by finding two numbers whose product is equal to the constant of the quadratic. Of those numbers, find the pair that adds to the coefficient of the x term of the quadratic; –4 and 3 multiply to –12 and add to –1. Therefore, the factors of x 2 – x – 12 are (x – 4) and (x + 3). Set each factor equal to 0 and solve for x: x – 4 = 0, x = 4, and x + 3 = 0, x = –3; x 2 – x = 12 when x equals 4 or –3. Trial and error (plugging each answer choice into the equation x 2 – x = 12) could be used, but only on a multiple-choice SAT question. It is important to be able to solve questions like this that could occur in the grid-in section of the SAT.

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