Question

Solve the equation by factoring, by finding square roots, or by using the quadratic formula. $$\frac{1}{16} s^{2}=4$$

Short answer

The solutions to the equation are \(s = 8\) and \(s = -8\)

Step-by-step solution

Simplifying the equation

Let's start by simplifying the equation. This is done by multiplying both sides of the equation by 16. This gives us \(s^{2} = 64\). This step is done because it allows to eliminate the fraction which simplifies the equation.

Take square roots

The next step is to take square roots of both sides of the equation. In this case, calculating the square root of \(s^{2}\) gives us \(s\) whereas the square root of 64 gives us ±8. So, we get \(s = ±8\). This reflects that there can be two possible solutions to the quadratic equation.