If (x – 7)(x – 5) = –1, what is the value of x?

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Accepted Answer

Use FOIL to multiply the binomials: (x – 7)(x – 5) = x 2 – 5x – 7x + 35 = x 2 – 12x + 35. Combine like terms on one side of the equation and set the expression equal to 0; x 2 – 12x + 35 = –1, x 2 – 12x + 36 = 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; –6 and –6 multiply to 36 and add to –12. Therefore, the factors of x 2 – 12x + 36 are (x – 6) and (x – 6). Since both factors are the same, set either factor equal to 0 and solve for x: x – 6 = 0, x = 6.

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