b Can you take a square root of a negative number?
A
a See solution.
B
bSolutions: x=11± sqrt(- 4) Are There No Solutions? There are two solutions, but they are complex.
Practice makes perfect
a The equation contains two parts: a square and a constant.
(x-11)^2_(square)+ 4_(constant) = 0
Let's focus on the expression on the left-hand side.
Regardless of what number we substitute for x, the square of it will always be positive. Therefore, the lowest value the square can take on is 0 when x is 11. For all other values, the square is positive.
x
(x-11)^2
=
9
( 9-11)^2
4
10
( 10-11)^2
1
11
( 11-11)^2
0
12
( 12-11)^2
1
13
( 13-11)^2
4
Since the square cannot be less than 0 and (x-11)^2 does not have a negative coefficient, we will have a lowest value of 4 when x= 11. Since 0 is smaller than 4, our equation has no solution.
b To solve the given equation, let's start by separating the square term. Then we will proceed further in order to isolate x.
