Question

solve for p.
36p² + 160 = 161
write your answer in simplified, rationalized form.
p = or p =

Explanation:

Step1: Isolate the quadratic term

Subtract 160 from both sides of the equation \(36p^{2}+160 = 161\).
\(36p^{2}=161 - 160\)
\(36p^{2}=1\)

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

Divide both sides by 36.
\(p^{2}=\frac{1}{36}\)

Step3: Take square roots

Take the square root of both sides. Remember that when taking the square root of a number, we consider both the positive and negative roots.
\(p=\pm\sqrt{\frac{1}{36}}\)
Simplify the square root. \(\sqrt{\frac{1}{36}}=\frac{\sqrt{1}}{\sqrt{36}}=\frac{1}{6}\)
So \(p = \frac{1}{6}\) or \(p=-\frac{1}{6}\)

Answer:

\(p=\frac{1}{6}\) or \(p = -\frac{1}{6}\)