Answer:
Explanation:
To solve the equation x2−2x−11=0
by completing the square, we need to follow these steps:
Add 11
to both sides of the equation to get x2−2x=11
Divide both sides by the coefficient of x2
, which is 1
, to get x2−2x=11
Take half of the coefficient of x
, which is −2
, and square it to get (−2/2)2=1
Add 1
to both sides of the equation to get x2−2x+1=12
Factor the left side of the equation as a perfect square to get (x−1)2=12
Take the square root of both sides of the equation to get x−1=±12
Add 1
to both sides of the equation to get x=1±12
Simplify the square root of 12
by dividing it by the largest perfect square factor, which is 4
, to get x=1±23
Write the final answer as two solutions: x=1+23
or x=1−23