SOLUTION: Solve the equation by making an appropriate substitution. Separate your answers with commas. x^{5/4}-14 x^{5/8} + 49 = 0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve the equation by making an appropriate substitution. Separate your answers with commas. x^{5/4}-14 x^{5/8} + 49 = 0      Log On


   

Question 945371: Solve the equation by making an appropriate substitution. Separate your answers with commas.
x^{5/4}-14 x^{5/8} + 49 = 0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
This is a quadratic equation.
z=x%5E%285%2F8%29
Then
z%5E2=x%5E%285%2F4%29
So,
z%5E2-14z%2B49=0
%28z-7%29%5E2=0
z-7=0
z=7
Substituting back,
highlight%28x=7%5E%288%2F5%29%29
That is, 7 to the 8%2F5 power.