SOLUTION: 16r^3-9r=0 solve please. thank you so much

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Question 297091: 16r^3-9r=0 solve please. thank you so much
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
16r^3 - 9r = 0

Factor out the r on the left side of the equation to get

r * (16r^2 - 9) = 0

r = 0 will satisfy this equation because anything times 0 equals 0.

16r^2 - 9 = 0 will also satisfy this equation because anything times 0 equals 0.

Solve for 16r^2 - 9 = 0

Add 9 to both sides of this equation to get 16r^2 = 9

Divide both sides of this equation by 16 to get r^2 = (9/16)

Take the square root of both sides of this equation to get r = +/- sqrt(9/16)

Since sqrt(9/16) is the same as sqrt(9) / sqrt(16), and since sqrt(9) = 3, and since sqrt(16) = 4, you get r = +/- 3/4

You have 3 possible answers to this equation.

They are:

r = 0
r = 3/4
r = -3/4

Plug those values into the original equation to see if they hold up.

Your original equation is 16r^3 - 9r = 0

When r = 0, this equation becomes 0 - 0 = 0 which is true.

When r = 3/4, this equation becomes 16*27/64 - 9*3/4 = 432/64 - 27/4 = 6.75 - 6.75 = 0 which is true.

When r = -3/4, this equation becomes 16*-27/64 + 9*3/4 = -432/64 + 27/4 = -6.75 + 6.75 = 0 which is true.

All 3 answers are solutions to the original equation.