If x 2 – 3x – 30 = 10, what is one possible value of x?

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Combine like terms on one side of the equation and set the expression equal to 0; x 2 – 3x – 30 = 10, x 2 – 3x – 40 = 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; –8 and 5 multiply to –40 and add to –3. Therefore, the factors of x 2 – 3x – 40 are (x – 8) and (x + 5). Set each factor equal to 0 and solve for x: x – 8 = 0, x = 8, and x + 5 = 0, x = –5; x 2 – 3x – 30 = 10 when x equals 8 or –5.

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