How do you solve this equation 4nsquared-81=0 using the quadratic formula?

Question

jim_thompson5910 · Answer

In the case of $$\Large 4n^2-81=0$$, its in the form $$\Large an^2+bn+c=0$$ where a = 4, b = 0 and c = -81


Now use the quadratic formula to solve


$$\Large n = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$$


$$\Large n = \frac{-(0)\pm\sqrt{(0)^2-4(4)(-81)}}{2(4)}$$


$$\Large n = \frac{0\pm\sqrt{0-(-1296)}}{8}$$


$$\Large n = \frac{\pm\sqrt{1296}}{8}$$


$$\Large n = \frac{\sqrt{1296}}{8} \ \text{or} \ n = \frac{-\sqrt{1296}}{8}$$


$$\Large n = \frac{36}{8} \ \text{or} \ n = \frac{-36}{8}$$


$$\Large n = \frac{9}{2} \ \text{or} \ n = \frac{-9}{2}$$



So the solutions are $$\Large n = \frac{9}{2} \ \text{or} \ n = \frac{-9}{2}$$