A rectangular auditorium seats 1170 people

A rectangular auditorium seats 1170 people. The number of seats in each row exceeds the number of rows by 9. Find the number of seats in each row.

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x = number of rows
x + 9 = number of seats in each row {number of seats in each row exceeds number of rows by 9}

seats in an auditorium = number of seats in each row multiplied by the number of rows

x(x + 9) = 1170 {total seats equals number of rows multiplied by the number of seats in each row}
x² + 9x = 1170 {used distributive property}
x² + 9x - 1170 = 0 {subtracted 1170 from each side}
(x + 39)(x - 30) = 0 {factored into two binomials}
x + 39 = 0 or x - 30 = 0 {set each factor equal to zero}
x = -39 or x = 30 {solved each equation for x}
x = 30 { number of rows cannot be negative}
x + 9 = 39 {substituted 30, in for x, into x + 9}

39 seats in each row

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