The square of a number is equal to two less than three times the number. What are two possible values of the number?

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Write an algebraic equation that describes the situation. If x is the number, then x 2 is the square of the number. Two less than three times the number is 3x – 2. Since the square of the number is equal to two less than three times the number, x 2 = 3x – 2. Combine like terms on one side of the equation and set the expression equal to 0; x 2 = 3x – 2, x 2 – 3x + 2 = 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; –1 and –2 multiply to 2 and add to –3. Therefore, the factors of x 2 – 3x + 2 are (x – 1) and (x – 2). Set each factor equal to 0 and solve for x: x – 1 = 0, x = 1, and x – 2 = 0, x = 2.

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