Answer:
Let x be the number
double x = 2 x
square the result (2x)^2
(2x)^2 - x subtract the original number
4 x^2 - x = 33
4 x^2 - x - 33 = 0
Solve the quadratic
(1 +- (1 + 4 * 132)^1/2) / 8
= (1 + 528^1/2) / 8 = (1 + 23) / 8 = 3 using the positive exponent
Check:
(2 * 3)^2 - 3 = 36 - 3 = 33
The answer is 35/12 and simplify that and u get 2 11/12.
To show my work apparently since the mods wont stop deleting my answers, here.
I first found a common denominator and use it to rewrite each fraction. Then I, subtracted the whole numbers and fractions separately.
Using the chain rule: The derivative of e^u is (e^u)(u'). Notice that e^u is rewritten exactly as is and then multiplied by the derivative of the exponent.
Let u=2x. So u'=2
So the derivative of e^u is e^(2x)*2 This can also be written as 2e^(2x).
