Question

given the equation ( x^2 - 16x + 20 = 0 ). what is the solution of the equation? use the keypad to enter your answer in the box. additional symbols can be found using the drop - down arrows at the top of the keypad.

Explanation:

Step1: Identify quadratic coefficients

For $ax^2+bx+c=0$, here $a=1$, $b=-16$, $c=20$.

Step2: Apply quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Step3: Calculate discriminant

$\sqrt{b^2-4ac}=\sqrt{(-16)^2-4(1)(20)}=\sqrt{256-80}=\sqrt{176}=4\sqrt{11}$

Step4: Substitute into formula

$x=\frac{16\pm4\sqrt{11}}{2}=8\pm2\sqrt{11}$

Answer:

$x=8+2\sqrt{11}$ and $x=8-2\sqrt{11}$