Question

There’s more anweser choices but please help me out

Answer 1

Check the picture below.

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{300}\\ a=\stackrel{adjacent}{270+x}\\ o=\stackrel{opposite}{100} \end{cases} \\\\\\ (300)^2= (270+x)^2 + (100)^2\implies 300^2=(270^2+540x+x^2)+100^2 \\\\\\ 300^2-100^2=270^2+540x+x^2\implies 300^2-100^2-270^2=540x+x^2 \\\\\\ 7100=x^2+540x\implies 0=x^2+540x-7100`

now, let's use the quadratic formula to get "x".

`~~~~~~~~~~~~\textit{quadratic formula} \\\\ 0=\stackrel{\stackrel{\textit{\small a}}{\downarrow }}{1}x^2\stackrel{\stackrel{\textit{\small b}}{\downarrow }}{+540}x\stackrel{\stackrel{\textit{\small c}}{\downarrow }}{-7100} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}`

`x= \cfrac{ - (540) \pm \sqrt { (540)^2 -4(1)(-7100)}}{2(1)} \implies x = \cfrac{ -540 \pm \sqrt { 291600 +28400}}{ 2 } \\\\\\ x= \cfrac{ -540 \pm \sqrt { 320000 }}{ 2 }\implies x= \cfrac{ -540 \pm 400\sqrt { 2 }}{ 2 } \implies x=-270\pm 200√(2) \\\\\\ x= \begin{cases} -270+ 200√(2)\\\\ -270- 200√(2) \end{cases}\implies x\approx \begin{cases} ~~ ~~ 12.84 ~~ \textit{\Large \checkmark}\\\\ -552.84 ~~ \bigotimes \end{cases}`

notice, "x" can't be negative.