2t^2/5 + 7t^1/5 + 3 = 0 #solve the equation by using substitution

Question

2t^2/5 + 7t^1/5 + 3 = 0 #solve the equation by using substitution 

Answer 1

Rewrite the equation so that we can use substitution.

 

2(t^1/5)² + 7t^1/5 + 3 = 0

 

 

Let      q = t^1/5

 

Then,

 

2q² + 7q + 3 = 0

 

 

Now we can solve.  Use FOIL.  If not, the use quadratic formula.

 

(2q + 1)(q + 3) = 0

 

 

Solving for q results in

 

q = -1/2       and      q = -3

 

 

Next, we substitute these q values into the original substitution to solve for t.  Since the original substitution has an odd root, these values will work out in the substitution.

 

t^1/5 = -1/2            and            t^1/5 = -3

 

Solve for t from these equations to get your actual solutions.