Answer
$x= 3,x= 17$
Work Step by Step
First transfer the constant to the right of the equal sign proceed with completing the square in line 1 of the equation by dividing the coefficient of the $20x$ term by $2$ ⁶and squaring it and adding the result on both sides.
$\begin{array}{rl}x^2-20 x+51 & =0 \\
x^2-20 x & =-51 \\
x^2-20 x+\left(\frac{20}{2}\right)^2 & =-51+\left(\frac{20}{2}\right)^2 \\
x^2-20 x+10^2 & =-51+10^2 \\
(x-10)^2 & =49 \\
x-10 & = \pm \sqrt{49} \\
x-10 & = \pm 7 \\ \text { Find the two separate solutions:} \\
x-10=7 & \ \text { or}\ \ x-10=-7 \\
x=7+10 & \ \text { or}\ \ x=-7+ 10 \\
x= 17 & \ \text { or}\ \ x = 3 \\
\end{array}$
Check
$$\begin{aligned}
17^2-20 (17)+51 & \stackrel{?}{ =}0\\
0& = 0\checkmark\\
3^2-20(3)+51 & \stackrel{?}{=}0\\
0&=0\checkmark.
\end{aligned}$$ The solution is $x= 3$, $x= 17$.
