Solving Simple Quadratic Equations Quick Check

Question

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Question
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

{−9}
left brace negative 9 right brace

{−9,9}
left brace negative 9 comma 9 right brace

There are no real solutions.
There are no real solutions.
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Answer 1

To solve the equation $x^2=81$ by inspection, we can take the square root of both sides. The equation implies that:

$$x=\pm \sqrt{81}$$

Calculating the square root, we find:

$$\sqrt{81}=9$$

Thus, the solutions are:

$$x=9\text{and}x=-9$$

Therefore, the complete solution set is:

$$-9,9$$

The correct response is:

$-9,9$