Answer :
form an equation using the information given.
x = number of sets in a row
x - 7 = number of rows
x(x - 7) = 638
x^2 - 7x = 638
make a quadratic equation
x^2 - 7x - 638 = 0
then solve either using quadratic equation or find two numbers that add to make -7 and multiply to make -638, one number is negative and one is positive, as the product of the numbers is negative.
-29 + 22 = -7
-29 x 22 = -639
then put into brackets
(x - 29)(x + 22) = 0
when the equation equals zero you can find two values for x
x = 29 or -22
x = number of sets in a row
x - 7 = number of rows
x(x - 7) = 638
x^2 - 7x = 638
make a quadratic equation
x^2 - 7x - 638 = 0
then solve either using quadratic equation or find two numbers that add to make -7 and multiply to make -638, one number is negative and one is positive, as the product of the numbers is negative.
-29 + 22 = -7
-29 x 22 = -639
then put into brackets
(x - 29)(x + 22) = 0
when the equation equals zero you can find two values for x
x = 29 or -22
rows =x
seats per row=x+7
and total seats = rows times seats per row or x(x+7) or x^2+7x=seats =638
so if you subtract 638 from both sides you can get an equation thatyou can factor out (x^2+7x-638)=0
638 factors out to 2 times 11 times 29 so
(x-22)(x+29)=0
so x-22=0
x=22
or x+29=0
x=-29 but you can't have a negative number of rows so this answer is wrong
so the answer is there are 22 rows and 29 seats (22+7=29)
seats per row=x+7
and total seats = rows times seats per row or x(x+7) or x^2+7x=seats =638
so if you subtract 638 from both sides you can get an equation thatyou can factor out (x^2+7x-638)=0
638 factors out to 2 times 11 times 29 so
(x-22)(x+29)=0
so x-22=0
x=22
or x+29=0
x=-29 but you can't have a negative number of rows so this answer is wrong
so the answer is there are 22 rows and 29 seats (22+7=29)
