Question

Sarah used the Quadratic Formula to solve the equation x² - 4x - 16 = 0. What should her solutions be?

Answer 1

Answer

x = (2 + 2√5)

OR

x = (2 - 2√5)

Explanation

In order to use the quadratic formula for the general quadratic equation,

ax² + bx + c = 0 is given as

$x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

For x² - 4x - 16 = 0,

a = 1

b = -4

c = -16

$\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(1\times-16)}}{2(1)} \\ x=\frac{4\pm\sqrt[]{16+64}}{2} \\ x=\frac{4\pm\sqrt[]{80}}{2} \\ \sqrt[]{80}=\sqrt[]{16\times5}=\sqrt[]{16}\times\sqrt[]{5}=4\sqrt[]{5} \\ x=\frac{4\pm\sqrt[]{80}}{2} \\ x=\frac{4\pm4\sqrt[]{5}}{2} \\ x=2\pm2\sqrt[]{5} \\ x=2+2\sqrt[]{5} \\ OR \\ x=2-2\sqrt[]{5} \end{gathered}$

Hope this Helps!!!