Answer :
We start with the equation
[tex]$$
7x^2 = 343.
$$[/tex]
Step 1. Isolate [tex]$x^2$[/tex]:
Divide both sides by [tex]$7$[/tex] to get
[tex]$$
x^2 = \frac{343}{7} = 49.
$$[/tex]
Step 2. Solve for [tex]$x$[/tex]:
We have
[tex]$$
x^2 = 49.
$$[/tex]
Taking the square root of both sides, we obtain
[tex]$$
x = \pm \sqrt{49}.
$$[/tex]
Since [tex]$\sqrt{49} = 7$[/tex], the solutions are
[tex]$$
x = 7 \quad \text{or} \quad x = -7.
$$[/tex]
Thus, the solutions to the equation are [tex]$7$[/tex] and [tex]$-7$[/tex].
In the provided list, this means the correct answers are those that represent [tex]$7$[/tex] (which can be written as [tex]$7$[/tex] or [tex]$\sqrt{49}$[/tex]) and [tex]$-7$[/tex] (which can be written as [tex]$-7$[/tex] or [tex]$-\sqrt{49}$[/tex]).
[tex]$$
7x^2 = 343.
$$[/tex]
Step 1. Isolate [tex]$x^2$[/tex]:
Divide both sides by [tex]$7$[/tex] to get
[tex]$$
x^2 = \frac{343}{7} = 49.
$$[/tex]
Step 2. Solve for [tex]$x$[/tex]:
We have
[tex]$$
x^2 = 49.
$$[/tex]
Taking the square root of both sides, we obtain
[tex]$$
x = \pm \sqrt{49}.
$$[/tex]
Since [tex]$\sqrt{49} = 7$[/tex], the solutions are
[tex]$$
x = 7 \quad \text{or} \quad x = -7.
$$[/tex]
Thus, the solutions to the equation are [tex]$7$[/tex] and [tex]$-7$[/tex].
In the provided list, this means the correct answers are those that represent [tex]$7$[/tex] (which can be written as [tex]$7$[/tex] or [tex]$\sqrt{49}$[/tex]) and [tex]$-7$[/tex] (which can be written as [tex]$-7$[/tex] or [tex]$-\sqrt{49}$[/tex]).
