Question

What numbet would beed to be added to complete the square?

Answer 1

169/4

1) Examining the quadratic x² -13x+ 31 = 0 and knowing that:

a= 1

b = -13

c =31

2) Then we can write the following number to add the next square

x² -13x+ 31 Pick that b coefficient and then divide it by 2

`\begin{gathered} x^2-13x+31=0 \\ x^2-13x\text{ =-31} \\ (x^{}-(13)/(2))^2=-31+(169)/(4) \\ (x^{}-(13)/(2))^2=(45)/(4) \\ \sqrt[]{(x^{}-(13)/(2))^2}=\sqrt[]{(45)/(4)} \\ x-(13)/(2)=\pm\frac{3\sqrt[]{5}}{2} \\ x_1=(13)/(2)+\frac{3\sqrt[]{5}}{2} \\ x_2=(13)/(2)-\frac{3\sqrt[]{5}}{2} \end{gathered}`

3) Hence the number that should be added to complete the square is 169/4 on both sides