How Do You Solve the Quadratic Equation \( X^2(2a - bX^2) = 2 \)?

[abhipatel]

X^2(2a – bX^2) = 2

value of constants can be pre-determined as a =0.8466 & b= 0.1733. Find X?

 

[Borek]

Substitute y=x²

 

[Mentallic]

$$x^{2}(2a-bx^{2})=2$$

let $$x^{2}=u$$

Substitute and expand - $$2au-bu^{2}=2$$

Rearrange into general form for quadratic format - $$bu^{2}-2au+2=0$$

Using the quadratic formula - $$u=\frac{2a\pm\sqrt{4a^{2}-8b}}{2b}$$

Substituing back for x, therefore - $$x=\pm\sqrt{\frac{2a\pm\sqrt{4a^{2}-8b}}{2b}}$$

Now just plug those values for a and b into the equation to get your solution(s) for x. Remember that if you encounter negatives in the surd parts, it means the solutions are imaginary and you will be left with 0 solutions. Unlikely to happen in this situation though.