Question

solve for n.
144n² - 16 = 0
write your answers as integers or as proper or improper fractions in simplest form.
n = or n =

Explanation:

Step1: Isolate the squared term

Add 16 to both sides of the equation \(144n^{2}-16 = 0\) to get \(144n^{2}=16\).

Step2: Solve for \(n^{2}\)

Divide both sides by 144: \(n^{2}=\frac{16}{144}\), simplify the fraction to \(n^{2}=\frac{1}{9}\).

Step3: Take square roots

Take the square root of both sides. Remember that \(\sqrt{x^{2}}=\pm x\), so \(n = \pm\sqrt{\frac{1}{9}}\). Since \(\sqrt{\frac{1}{9}}=\frac{1}{3}\), we have \(n=\frac{1}{3}\) or \(n = -\frac{1}{3}\).

Answer:

\(n=\frac{1}{3}\) or \(n = -\frac{1}{3}\)