Find all real solutions of the equation by completing the square. x2 + 6x − 12 = 0

To complete the square we:

Move the non-x tern to the right  x^2 + 6c = 12

Divide the equation by the coefficient of x^2 (already done)

Next we take the coefficient of x, divide it by 2, square it, then add it to both sides.

6 / 2 = 3 then 3^2 = 9 then adding to both sides

x^2 + 6x + 9 = 12 +9

(x+3)^2 = 21 then taking the square root of both sides:

x + 3 = square root (21)

x = square root (21) -3  equals 4.582575695 -3

x1 = 1.582575695

AND remebering the square root (21) also = -4.582575695 then

x2 = -7.582575695

Source: 1728.com/quadr2.htm

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺

look at the picture i have filled out a table for it. hope this .