Question

-X² + 5x - 6 = 2 Using the quadratic formula

Answer 1

$-x^2+5x-6=2\\-x^2+5x-6-2=0\\-x^2+5x-8=0$

↝ Form into $ax^2+bx+c = 0$ where a > 0 (Optional)

$x^2-5x+8=0$ ↝ Multiply -1 for both sides.

↝ Then proceed with the Quadratic Formula.

x = [-b ± (√b²-4ac)]/2a ↝ Quadratic Formula

$x=\frac{-(-5)+-\sqrt{(-5)^2-4(1)(8)}}{2(1)}\\x=\frac{5+-\sqrt{25-32}}{2}$

↝ As you can see that inside the square root, the numbers cannot be negative. Therefore, the solutions are imaginary.

↝ Solution with Real Numbers  System ↝  There are no real solutions.

↝ Solution with Complex Number System ↝

$x=\frac{5+-\sqrt{25-32}}{2}\\x=\frac{5+-\sqrt{-7}}{2}\\x=\frac{5+-\sqrt{7}i }{2}$

Therefore, the answer for Complex Number System is (5±√7i)/2