Answer:
[tex]x = 1+ i\sqrt{19},1- i\sqrt{19}[/tex]
Step-by-step explanation:
Given : [tex]x^2+20=2x[/tex]
To Find: using the quadratic formula find x'
Solution:
Quadratic equation : [tex]ax^2+bx+c=0[/tex] ---1
Quadratic Formula : [tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
We are given : [tex]x^2+20=2x[/tex]
[tex]x^2-2x+20=0[/tex]
On comparing with 1
a = 1
b = -2
c = 20
Substitute the values in the formula .
[tex]x = \frac{-(-2)\pm\sqrt{(-2)^2-4(1)(20)}}{2(1)}[/tex]
[tex]x = \frac{2\pm\sqrt{4-80}}{2}[/tex]
[tex]x = \frac{2\pm\sqrt{-76}}{2}[/tex]
[tex]x = \frac{2\pm\sqrt{i^2 (2)(2)(19)}}{2}[/tex]
[tex]x = \frac{2\pm 2i\sqrt{19}}{2}[/tex]
[tex]x = 1\pm i\sqrt{19}[/tex]
[tex]x = 1+ i\sqrt{19},1- i\sqrt{19}[/tex]
Hence The values of x are [tex]x = 1+ i\sqrt{19},1- i\sqrt{19}[/tex]
