Question

x² - 12x + 45 = 0

Explanation:

Step1: Identify quadratic coefficients

For $ax^2+bx+c=0$, $a=1$, $b=-12$, $c=45$

Step2: Calculate discriminant

$\Delta = b^2-4ac = (-12)^2 - 4(1)(45)$
$\Delta = 144 - 180 = -36$

Step3: Apply quadratic formula

$x = \frac{-b\pm\sqrt{\Delta}}{2a} = \frac{12\pm\sqrt{-36}}{2}$

Step4: Simplify complex roots

$\sqrt{-36}=6i$, so $x=\frac{12\pm6i}{2}=6\pm3i$

Answer:

$x=6+3i$ and $x=6-3i$