Question

Why does (x-2)^2+9=0 have no real solutions?

Answer 1

see explanation

Explanation:

Given

(x - 2)² + 9 = 0 ( subtract 9 from both sides )

(x - 2)² = - 9 ( take the square root of both sides )

x - 2 = ±
`√(-9)`

`√(-9)` yields no real solutions

There is no real number when multiplied by itself gives - 9

In fact the solutions to
`√(-9)` are said to be imaginary, that is ± 3i

where i =
`√(-1)`

If interested investigate further.