How do you solve #10x^2-15x=0# using any method?

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
JJ
Aug 24, 2017

#x=0, 3/2#

Explanation:

First, let's factor out like terms. In this equation, #5x# is common between the two terms on the left.

#10x^2-15x=0 ->#

#5x(2x-3)=0#

Now that you got it factored, you need to set #5x=0# and #2x-3=0#. Note that #5x# snd #2x-3# give you your zeroes for this equation.

#5x=0 ->#

#x=0# Here is our first value for x.

#2x-3=0 ->#

#x=3/2# Here is our second value for x.

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