Question

(18 + x)^2 = (x + 6)^2 + (243/12+x)^2
x=?​

Answer 1

The final value of $x= \frac{-264 \pm \sqrt{-55296}}{32}$

Step-by-step explanation:

$\ Given \ value:\\\\(18 + x)^2 = (x + 6)^2 + (\frac{243}{12}+x)^2\ find:\\\\x= ?\\\\\ Solution:\\\\(18 + x)^2 = (x + 6)^2 + (\frac{243}{12}+x)^2\ formula:\\\\ (a+b)^2= a^2+b^2+2ab \\\\\rightarrow 18^2+ x^2+36x= x^2+36+12x+ (\frac{243}{12})^2+ x^2+ 2(\frac{243}{12})x \\\\\rightarrow 324+ x^2+36x= x^2+36+12x+ \frac{59049}{144}+ x^2+ \frac{243}{6}x \\\\\rightarrow 324+ x^2+36x= 2x^2+ \frac{64233}{144}+ \frac{315x}{6} \\\\\rightarrow 2x^2+ \frac{64233}{144}+ \frac{315x}{6} -324- x^2-36x = 0$

$\rightarrow x^2+ \frac{64233}{144}+ \frac{315x}{6} -324-36x = 0 \\\\\rightarrow x^2+ \frac{17577}{144}+ \frac{99x}{6} = 0 \\\\\rightarrow \frac{864x^2+105462+14256x}{864} = 0 \\\\\rightarrow 864x^2+105462+14256x = 0$

$\rightarrow 2(432x^2+52731+7128x) =0\\\\\rightarrow 432x^2+7128x+52731=0\\\\\rightarrow 27(16x^2+264x+1953)=0\\\\\rightarrow 16x^2+264x+1953 =0\\\\ \ compare \ the \ value \ ax^2+bx+c=0\\\\a= 16\\b=264\\c=1953\\\ Formula:\\\\x= \frac{-b \pm \sqrt{b^2-4ac}}{2a} \\\\x= \frac{-264 \pm \sqrt{-55296}}{32}$

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