Question

1. $8n^2 - 2 = 734$

Explanation:

Step1: Isolate the quadratic term

Add 2 to both sides of the equation \(8n^{2}-2 = 734\) to get \(8n^{2}=734 + 2\).
Simplifying the right side, we have \(8n^{2}=736\).

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

Divide both sides of the equation \(8n^{2}=736\) by 8. So, \(n^{2}=\frac{736}{8}\).
Calculating the right side, we get \(n^{2}=92\).

Step3: Solve for \(n\)

Take the square root of both sides. Remember that when we take the square root of a number, we have two solutions (positive and negative). So, \(n=\pm\sqrt{92}\).
Simplify \(\sqrt{92}\) as \(\sqrt{4\times23}=2\sqrt{23}\). So, \(n = \pm2\sqrt{23}\) or approximately \(n\approx\pm9.59\).

Answer:

\(n = 2\sqrt{23}\) or \(n=-2\sqrt{23}\) (or approximately \(n\approx9.59\) or \(n\approx - 9.59\))