Question

1. solve for p:

$4(p^2 - 2) = 568$
12
$p = 12$
$p = 12$
$p = -12$
12
enter your next step here

Explanation:

Step1: Divide both sides by 4

To isolate the quadratic term, we divide both sides of the equation \(4(p^{2}-2) = 568\) by 4.
\(\frac{4(p^{2}-2)}{4}=\frac{568}{4}\)
Simplifying both sides, we get \(p^{2}-2 = 142\).

Step2: Add 2 to both sides

Next, we add 2 to both sides of the equation \(p^{2}-2=142\) to solve for \(p^{2}\).
\(p^{2}- 2+2=142 + 2\)
Simplifying, we have \(p^{2}=144\).

Step3: Take square root of both sides

To solve for \(p\), we take the square root of both sides of the equation \(p^{2}=144\).
\(p=\pm\sqrt{144}\)
Since \(\sqrt{144} = 12\), we get \(p = 12\) or \(p=- 12\).

Answer:

\(p = 12\) or \(p=-12\)