Use inspection to solve the equation x2=81 , then select the complete solution set below. If there are no real solutions, select “There are no real solutions.”(1 point) Responses {9} left brace 9 right brace There are no real solutions. There are no real solutions. {−9,9} left brace negative 9 comma 9 right brace {−9}
To solve the equation x^2 = 81, we take the square root of both sides of the equation.
√(x^2) = ±√81
Since the square root of a number is non-negative, we can simplify this to:
x = ±9
Therefore, the complete solution set is {−9, 9}.
To solve the equation x^2 = 81 using inspection, we can take the square root of both sides of the equation.
√(x^2) = √81
Simplifying, we get:
|x| = 9
Since the absolute value of x can be either positive or negative, the solution set for this equation is:
{-9, 9}
Therefore, the correct answer is:
{−9, 9} (negative 9, 9)
To solve the equation x^2 = 81 using inspection, we need to find the numbers that, when squared, equal 81.
1. First, we know that both positive and negative numbers can square to the same result. So, we will consider both possibilities.
2. We can start by taking the square root of 81, which is 9. This means that one possible solution is x = 9.
3. Similarly, the negative square root of 81 is -9. Therefore, -9 is also a possible solution.
Hence, the complete solution set for the equation x^2 = 81 is {9, -9}, which means that the correct option is {−9, 9}.