If (x – 2)(x + 6) = –16, what is the value of x?

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Accepted Answer

Use FOIL to multiply the binomials: (x – 2)(x + 6) = x 2 + 6x – 2x – 12 = x 2 + 4x – 12. Combine like terms on one side of the equation and set the expression equal to 0; x 2 + 4x – 12 = –16, x 2 + 4x + 4 = 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; 2 and 2 multiply to 4 and add to 4. Therefore, the factors of x 2 + 4x + 4 are (x + 2) and (x + 2). Since both factors are the same, set either factor equal to 0 and solve for x: x + 2 = 0, x = –2.

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