Solve x2 − 8x + 5 = 0 using the completing-the-square method.
x = negative four plus or minus the square root of eleven
x = four plus or minus the square root of eleven
x = negative four plus or minus the square root of five
x = four plus or minus the square root of five

Option 2

Step-by-step explanation:

We have been given a quadratic equation

First step in completing method square is to make the coefiicient of    1

Since, in given quadratic equation coefficient of is already 1. we will proceed to the next step which is add and subtract square of the half of coefficient of x in given quadratic equation.

Here, half of coefficient of x that is  8 would be 4 so we will add and subtract in given quadratic equation we will get

 

Now, we will proceed to the third step that is making the whole square formula according to the terms

Here, we can see that we are geeting the formula of from

The equation will become

After simplifying we will get  

After further simplification we will get

After more simplification we will get

Hence, we will get the value of x which is

A)
for option 1, the type of function is linear because the series of interest earned increases arithmetically in $110 per year.
for option 2, the type of function is exponential because the series of interest earned increases geometrically in $1.09 per year.

b)
the option 1 refers to a simple interest with a function: f(n) = $1000 + $100n
the option 2 refers to a compound interest with a function: f(n) = $1000  * (1.09) ⁿ
c)
after 20 years, she would get:
in option 1, f(20) = $1000 + $110*20 = $3200
in option 2, f(20) = $1000 * (1.09)² ⁰ = $5604.41
there is a significant difference between these options because the interest earned (through compound interest) accrues on the principal amount and the accumulated interest of previous periods.