Question #3c21d

Let me start by rewriting the five lines

`"L1: " 4s^2 - 40s + 100 = 0`

`"L2: " s^2 - 10s + 25 = 0`

`"L3: " s = (-10 +- sqrt( 10^2 - 4 * 1 * 25))/(2 * 1)`

`"L4: " s = (-10 +- 0)/2`

`"L5: " s = -10/2`

`"L6: " s = -5`

`color(white)(aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa)/color(white)(a)`

The way I see it, the error occurs in line `3`, `"L3"`. Here's why.

Your starting quadratic equation looks like this

`4s^2 - 40s + 100 = 0`

To get to `"L2"`, you need to divide all the terms by `4`

`(color(red)(cancel(color(black)(4)))s^2)/color(red)(cancel(color(black)(4))) - (40s)/4 + 100/4 = 0`

`s^2 - 10s + 25 = 0`

So far, so good. Now comes the interesting part. You can get to line `3` by using the quadratic formula, which for a general form quadratic equation

`color(blue)(ax^2 + bx + c = 0)`

takes the form

`color(blue)(|bar(ul(color(white)(a/a)x_(1,2) = (-b +- sqrt(b^2 - 4 * a * c))/(2 * a) color(white)(a/a)|)))`

For your quadratic, you have

`{(a = 1), (b = -10), (c = 25) :}`

This means that line `3` should read

`s_(1,2) = (- (-10) +- sqrt( (-10)^2 - 4 * 1 * 25))/(2 * 1)`

As you can see, your example uses `b = 10` instead of `b = -10`. This represents the first mistake made when trying to solve this quadratic. From this point on, all the remaining lines are incorrect.

Therefore, you should have

`"L3: " s_(1,2) = (- (-10) +- sqrt( (-10)^2 - 4 * 1 * 25))/(2 * 1)`

`"L4: " s_(1,2) = (10 +- 0)/2`

`"L5: " s = 10/2`

`"L6: " s = 5`