Question

Find all real and imaginary solutions of the equation. x² + 4x =(2x+1)²

Answer 1

Hi,

Explanation:

`x^2+4x=(2x+1)^2\\x^2+4x=4x^2+4x+1\\3x^2+1=0\\3x^2-i^2=0\\\\(√(3)x+i) (√(3)x-i) =0\\\\x=(-i)/(√(3))\ or\ x=(i)/(√(3)) \\\\\\\boxed{x=(i√(3) )/(3) \ or\ x=(-i√(3) )/(3) }`

There are only 2 imaginary solutions and no real solution.