how do I get to the answer 2.49 from (2.279x^2)^2 +(5.096x)^2 = 19^2?

Question

x = 2.49

Answer 1

well,
(2.279x^2)^2 = 5.1938x^4
(5.096x)^2 = 25.9692x^2

So, now you have

5.1938x^4 + 25.9692x^2 - 361 = 0

Use the quadratic formula to find x^2:

x^2 = (-25.9692±√(25.9692^2+4*5.1938*361))/(2*5.1938)

one of your answers will be

x^2 = 6.20378
so, x = ±2.49