enter the correct answer in the box. what are the solutions of this quadratic equation? $x^{2}=16x - 65$…

enter the correct answer in the box. what are the solutions of this quadratic equation? $x^{2}=16x - 65$ substitute the values of a and b to complete the solutions. $x = a+bi$ $x = a - bi$

enter the correct answer in the box. what are the solutions of this quadratic equation? $x^{2}=16x - 65$ substitute the values of a and b to complete the solutions. $x = a+bi$ $x = a - bi$

Answer

Answer:

$x = 8 + 1i$, $x = 8 - 1i$

Explanation:

Step1: Rewrite in standard form

$x^{2}-16x + 65=0$

Step2: Identify coefficients

$a = 1$, $b=-16$, $c = 65$

Step3: Use quadratic formula

$x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}=\frac{16\pm\sqrt{(-16)^{2}-4\times1\times65}}{2\times1}$

Step4: Calculate discriminant

$\sqrt{(-16)^{2}-4\times1\times65}=\sqrt{256 - 260}=\sqrt{-4}=2i$

Step5: Find solutions

$x=\frac{16\pm2i}{2}=8\pm i$