Solve for v in v^2 - (v/4)^2 = 196

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SUMMARY

The equation v^2 - (v/4)^2 = 196 can be solved by correctly applying the square to the fraction (1/4). The initial attempt incorrectly simplified the equation to v^2(1 - (1/4)) = 196, leading to an erroneous calculation of v. The correct approach involves recognizing that (v/4)^2 equals v^2/16, which must be properly accounted for in the equation. The final solution for v is approximately 16.17, but this value is derived from an incorrect simplification.

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Homework Statement



I'm solving for v in:

v^2 − (v/4)^2 = 196

Homework Equations





The Attempt at a Solution



→v^2(1-(1/4))=196

→v^2(.75)=196 → √(196/.75)≈16.17

What did I do wrong?
I know this isn't the right answer, but why?
 
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You did something wrong with this part of the equation

(v/4)^2
 
2milehi said:
You did something wrong with this part of the equation

(v/4)^2

I forgot to square the (1/4)! how silly of me.
Thank you!
 

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