Consider the following quadratic equation.
(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?
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.
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 (x + 3)^2 = 43, the result is x + 3 = ±√43. This gives two possible solutions for x: x = -3 + √43 and x = -3 - √43. Therefore, the equation has two real solutions.