How do you solve for x in this complex problem?

Question

2.4 * 1/2 * (x^2 + 25)^(-1/2) * 2x - 1 = 0

killing me. ughhh

Answer 1

let's simplify it a little:

2.4[(x² + 25)^(-1/2)]x = 1
2.4x / √(x² + 25) = 1
2.4x = √(x² + 25)
5.76x² = x² + 25
4.76x² = 25
x² = 2500/476 = 625/119
x = ±25/√119
x = ±(25/119)√119

Answer 2

2.4 * 1/2 * (x^2 + 25)^(-1/2) * 2x - 1 = 0
Let the 1/2 and the 2 from the 2x cancel out, and move the 1 over to the other side:
=> 2.4 * (x^2 + 25)^(-1/2) * x = 1
Multiply by √(x^2 + 25):
=> 2.4 x = √(x^2 + 25)
Square both sides - note that since the RHS must be positive, we need to restrict ourselves to solutions where x is positive too (else the LHS would be negative).
=> 5.76 x^2 = x^2 + 25
=> 4.76 x^2 = 25
=> x = 5 / √4.76 (taking only the positive root, as noted earlier)
= 25 / √119.

Answer 3

Grind it out ... simplifying to start:
x/sqrt(x^2+25) = 1/2.4
(x^2+25)/x^2 = 2.4^2
1+25/x^2 = 2.4^2
25 = 4.76x^2
x = + 5/sqrt(4.76)

Answer 4

2.4 x 1/2 x 2x = 2.4x

2.4x ( 1/ sq. rt (x^2+25) ) -2 = 0
Square everything now
4.16x^2 (1/(x^2 +25) ) - 4 =0

4.16x^2/ (x^2 +25) = 4
4x^2 + 100= 4.16x^2
100= .16x^2
x= sq. root of 100/.16