Question

Solve the equation: -149=x^2-24x

Answer 1

$-149=x^2-24x \\\\ x^2-24x+149=0 \\\\ a=1 \\ b=-24 \\ c=149 \\\\ \Delta=(-24)^2 -149*4= 576-596\to \boxed{-20} \\\\ x_1;x_2= \frac{-(-24)+ /-1 \sqrt{20}}{2} = \frac{24+/- 2i\sqrt{5}}{2} \\\\ x_1= \frac{24+2i\sqrt{5}}{2}= \frac{2(12+i\sqrt{5})}{2} \to\boxed{\boxed{12+i\sqrt{5}}} \\\\ x_2=\frac{24-2i\sqrt{5}}{2}=\frac{2(12-i\sqrt{5}}{2}\to\boxed{\boxed{12-i\sqrt{5}}}$

Answer 2

$-149=x^2-24x\\ x^2-24x+149=0\\ x^2-24x+144+5=0\\ (x-12)^2=-5\\ x-12=-\sqrt{-5} \vee x-12=\sqrt{-5}\\ x=12-\sqrt{5}i \vee x=12+\sqrt{5}i$