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

  • Thread starter physicsdreams
  • Start date
In summary, the conversation discusses solving the equation v^2 - (v/4)^2 = 196 for v. This can be done using the quadratic formula or by factoring the equation. The quadratic formula is v = (-b ± √(b^2-4ac)) / 2a and factoring the equation involves rewriting it as (v+14)(v-14) = 0 and solving for v by setting each factor equal to 0. The possible solutions for v are v = ±14 or v = ±56.
  • #1
physicsdreams
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0

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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  • #2
You did something wrong with this part of the equation

(v/4)^2
 
  • #3
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!
 

1. What is the equation being solved in this problem?

The equation being solved is v^2 - (v/4)^2 = 196.

2. How do you solve for v in this equation?

To solve for v, you can use the quadratic formula or factor the equation.

3. What is the quadratic formula?

The quadratic formula is v = (-b ± √(b^2-4ac)) / 2a, where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.

4. How do you factor the equation to solve for v?

To factor the equation, you can rewrite it as (v+14)(v-14) = 0 and then solve for v by setting each factor equal to 0.

5. What are the possible solutions for v in this equation?

The possible solutions for v are v = ±14 or v = ±56.

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