Question
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Answer
\( p = -2\sqrt{21} \) or \( p = 2\sqrt{21} \)
Solution
Solve the equation \( 168=2p^{2} \).
Solve the quadratic equation by following steps:
- step0: Solve using square roots:
\(168=2p^{2}\)
- step1: Swap the sides:
\(2p^{2}=168\)
- step2: Divide both sides:
\(\frac{2p^{2}}{2}=\frac{168}{2}\)
- step3: Divide the numbers:
\(p^{2}=84\)
- step4: Simplify the expression:
\(p=\pm \sqrt{84}\)
- step5: Simplify the expression:
\(p=\pm 2\sqrt{21}\)
- step6: Separate into possible cases:
\(\begin{align}&p=2\sqrt{21}\\&p=-2\sqrt{21}\end{align}\)
- step7: Rewrite:
\(p_{1}=-2\sqrt{21},p_{2}=2\sqrt{21}\)
The solutions to the equation \(168=2p^{2}\) are \(p=-2\sqrt{21}\) and \(p=2\sqrt{21}\).
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Simplify this solution Extra Insights
To solve for \( p \) in the equation \( 168 = 2p^2 \), first divide both sides by 2, giving you \( 84 = p^2 \). Next, take the square root of both sides, which leads to \( p = \sqrt{84} \). Simplifying \( \sqrt{84} \) further, we get \( p = \sqrt{4 \times 21} = 2\sqrt{21} \). Therefore, the value of \( p \) is \( 2\sqrt{21} \). You could also estimate \( \sqrt{21} \) since it's a bit more than 4 (because \( 4^2 = 16 \) and \( 5^2 = 25 \)), making \( p \) about \( 2 \times 4.58 \approx 9.16 \). Fun fact: \( \sqrt{21} \) is an irrational number, which means it can't be exactly expressed as a simple fraction, giving it a special place in the world of mathematics!
