Question

1. solve for p:

4(p² - 2) = 568
enter your next step here

Explanation:

Step1: Divide both sides by 4

To isolate the expression with \( p \), we divide both sides of the equation \( 4(p^2 - 2)=568 \) by 4. This gives us \( \frac{4(p^2 - 2)}{4}=\frac{568}{4} \), which simplifies to \( p^2 - 2 = 142 \).

Step2: Add 2 to both sides

Next, we add 2 to both sides of the equation \( p^2 - 2 = 142 \) to isolate \( p^2 \). So, \( p^2 - 2 + 2 = 142 + 2 \), which simplifies to \( p^2 = 144 \).

Step3: Take square root of both sides

To solve for \( p \), we take the square root of both sides of the equation \( p^2 = 144 \). Remembering that the square root of a number has two solutions (positive and negative), we get \( p=\pm\sqrt{144} \), which simplifies to \( p = \pm 12 \).

Answer:

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