Consider the following quadratic equation.

Question

(x + 3)2 = 43
When taking the square root of both sides of this equation, how many solutions will the equation have? How do you know? show your work
A) This equation has one real solution with a positive sign in √43.
B) This equation has two real solutions, because when taking the square root of 43, there is a positive and a negative solution for ±√43.
C) This equation has one real solution with a negative sign in √43.
D) This equation has no real solutions.

Answer 1

B) This equation has two real solutions, because when taking the square root of 43, there is a positive and a negative solution for ±√43.

When taking the square root of both sides of the equation, we get:

x + 3 = ±√43

This means that x = -3 + √43 and x = -3 - √43 are the two real solutions to the equation. Therefore, the equation has two real solutions.