As a refresher, I was skimming through a free Calculus online textbook "MOOCULUS massive open online calculus" (https://mooculus.osu.edu/handouts) and stumbled upon the following example solving a quadratic equation via the quadratic formula:
Is the step where they get rid of the -10 in the denominator correct? I am wondering because sqrt(81)/10 is != sqrt(8.1) for example.
It is correct. $$t=\dfrac{-30\pm \sqrt{30^2-4(-5)(60-h)}}{2(-5)}$$ $$t=\dfrac{-30\pm \sqrt{900+20(60-h)}}{-10}$$ $$t=\dfrac{-30\pm \sqrt{900+1200-20h}}{-10}$$ $$t=\dfrac{-30\pm \sqrt{2100-20h}}{-10}$$ $$t=\dfrac{-30}{-10}\pm \dfrac{\sqrt{2100-20h}}{-10}$$ $$t=3 \mp \dfrac{\sqrt{2100-20h}}{10}$$ $$t=3 \mp \dfrac{\sqrt{2100-20h}}{\sqrt{100}}$$ $$t= 3 \mp \sqrt{\dfrac{2100-20h}{100}}$$ $$\displaystyle \large \boxed{t= 3\mp \sqrt{21-0.2h}}$$ I hope this post helped you.