NotThatSmart

This isn't hard to do, we just have to set up an equation. 

First, let s be the sidenlength of a equation. 

\(s^2 = 10s + 38 \\ s^2 - 10s = 38 \\ s^2 -10s + 25 = 38 + 25\)

\((s - 5)^2 = 63 \)

\(s - 5 = \sqrt{63}\)

\(s = \sqrt{63} + 5\)

The other possible equation would get a negative value, but a sidlength can't be negative, so we reject that possibility. 

So we have \(s = \sqrt{63} + 5\)

Thanks! :)

Not too bad of a question. 

\(\Delta EFG \cdot \frac{2h}{3}=18\\ \Delta EFG =\frac{3\cdot 18}{2h}\\ [{EFGH}]=\Delta EFG\cdot \frac{1}{3}h\\ [{EFGH}]=\frac{3\cdot 18}{2h}\cdot \frac{1}{3}h\\ [{EFGH}]=9\)

Let's first find u and v. Carrying all terms to one side and combining like terms, we get \(x^2-6x+13=0\)

Using the quadratic equation, we get \(x=3+2i,\:x=3-2i\), meaning we have \(u =3-2i\) and \(v =3+2i\).

Plugging these values into \(u/v^2 + v/u^2\), we get \(\frac{3-2i}{(3+2i)^2} + \frac{3+2i}{(3-2i)^2}\)

Simplifying the expression gets us the fraction \(-\frac{18}{169}\)

Thanks! :)

Combining all the like terms, we have \(2x^2-4x-68=0\). 

Using the qudratic equation to find x, we come up with \(x=1+\sqrt{35},\:x=1-\sqrt{35}\)

This problem isn't hard really, It's just moving all terms to one side and combining like terms, before using the quadratic equation to find x. 

Thanks! :)

The value of b in z^2 + bz + c = 0 is equal to the sum of the two roots. 

It's just 4+2i + (-5)+8i = -1+10i

Thanks! :)