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

1 Answer
May 8, 2017

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)