Question

How do you solve `(s+1)^2/10-12/5=15/2`?

Answer 1

`s = -1+-3sqrt(11)`

Explanation:

Given:

`((s+1)^2)/(10)-12/5=15/2`

We want to isolate the `(s+1)^2` term in order to solve for s

First add `12/5` to both sides:

`((s+1)^2)/(10)-12/5color(red)(+12/5)=15/2color(red)(+12/5)`

On the left hand side, the `-12/5` and `+12/5` add to `0`:

`((s+1)^2)/(10)cancel(-12/5)cancel(color(red)(+12/5))=15/2color(red)(+12/5)`

And on the right hand side, we need to find a common denominator to add the fractions:

`((s+1)^2)/(10)=15/2color(red)((5/5))+12/5color(red)((2/2))`

`((s+1)^2)/(10)=color(red)(75/10)+color(red)(24/10) = 99/10`

Next we multiple both sides by 10 to isolate the `(s+1)^2` term

`color(red)(10)((s+1)^2)/(10) = color(red)(10) 99/10`

Which gives

`(s+1)^2 = 99`

Square root both sides of the equation

`sqrt((s+1)^2) = sqrt(99)`

Which gives

`s+1 = +-sqrt(99)`

NOTE: When taking the square root of any term, the answer can be both negative (-) and positive (+). When you raise a negative number to the second (2) power, the negative multiplies out to give a positive answer.

Now, simplifying the answer, and subtracting 1 from both sides

`s +1 color(red)(-1) = +-sqrt((9)(11)) color(red)(-1)`

9 is a perfect square, with a square root value of 3, so the answer can be simplified to

`s = -1+-3sqrt(11)`