Question

What value is added to both sides of the equation x2 − 2x = 10 in order to solve by completing the square?

A. -1
B. -2
C. 1
D. 2

Answer 1

Hi,
Answer C

$x^2-2x=10\\ x^2-2x+1=10+1\\ \Rightarrow\ (x-1)^2=11\\ \Rightarrow\ (x-1)^2-11=0\\ \Rightarrow\ (x-1)^2-( \sqrt{11})^2=0\\ \Rightarrow\ ((x-1)+ \sqrt{11})((x-1)- \sqrt{11})=0\\ \Rightarrow\ x-1+ \sqrt{11}=0\ or\ x-1- \sqrt{11}=0\\ \Rightarrow\ x=1- \sqrt{11}\ or\ x=1+ \sqrt{11}$