How do you solve 15x^(-2)+7x^(-1)-2=0?

1 Answer
Nov 6, 2015

Multiply through by x^2 to turn it into a standard quadratic equation, and then solve with the quadratic formula

Explanation:

First, we multiply each side of the equation by x^2.

x^2(15x^-2 + 7x^-1 - 2) = 0x^2
=>15 + 7x - 2x^2 = 0 (by applying the rule x^a * x^b = x^(a+b))

Rearranging the terms gives us a familiar quadratic form.

-2x^2 + 7x + 15 = 0

Finally, we apply the quadratic formula x = (-b +- sqrt(b^2 -4ac))/(2a) where a = -2, b = 7, and c = 15

This gives

x = -3/2 or x = 5.