(x+2)^2=-7 solvve

Question

please show me step by step how to solve this equation. I need to know the square root property.

thank you

Sonya

Answer 1

(x+2)^2 = -7

 

sqrt((x+2)^2) = sqrt(-7)

|x+2| = sqrt(-1)*sqrt(7)

sqrt(-1) is the imaginary unit that we call "i" (lower case eye)

 

|x+2| = i*sqrt(7)

x+2 = ± i*sqrt(7)

x = -2 ± i*sqrt(7)

Answer 2

Hi Sonya;

(x+2)²=-7

Let's take the square root of both sides...

√[(x+2)²]=√-7

+/-(x+2)=√-7

(x+2)=+/-√-7

The result of a square-root of a negative number is an imaginary number.

7 is a prime number.

If the result was +/-√-4, then the following result would be +/-2i, with the i indicating it is imaginary.