Question

Find the radius of a circle with an area of pie (16x^2+40x+25)

Answer 1

`\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ A=(16x^2+40x+25)\pi \end{cases}\implies (16x^2+40x+25)\pi =\pi r^2 \\\\\\ \cfrac{(16x^2+40x+25)\pi }{\pi }=r^2\implies 16x^2+40x+25=r^2 \\\\[-0.35em] ~\dotfill`

`\bf \begin{cases} (4x)(4x)=&\stackrel{first~term}{16x^2}\\\\ (5)(5)=&\stackrel{constant}{25}\\\\ (4x)(5)+(4x)(5)=&\stackrel{middle~term}{40x} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 16x^2+40x+25=r^2\implies (4x+5)(4x+5)=r^2 \\\\\\ (4x+5)^2=r^2\implies √((4x+5)^2)=r\implies 4x+5=r`