Question

using the quadratic formula to solve ( x^{2}+20 = 2x ), what are the values of ( x )?
( 1pmsqrt{21}i )
( -1pmsqrt{19}i )
( 1pm2sqrt{19}i )
( 1pmsqrt{19}i )

Explanation:

Step1: Rearrange to standard form

$x^2 - 2x + 20 = 0$

Step2: Identify coefficients

$a=1,\ b=-2,\ c=20$

Step3: Apply quadratic formula

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Step4: Calculate discriminant

$b^2-4ac=(-2)^2-4(1)(20)=4-80=-76$

Step5: Simplify square root

$\sqrt{-76}=\sqrt{4\times(-19)}=2\sqrt{19}i$

Step6: Substitute and simplify

$x=\frac{2\pm2\sqrt{19}i}{2}=1\pm\sqrt{19}i$

Answer:

$1\pm\sqrt{19}i$ (matches the last option: $1\pm\sqrt{19}i$)