Question

If using the method of completing the square to solve the quadratic equation

x2 -9x + 2 = 0, which number would have to be added to "complete the square"?

Answer 1

Add the square of half of the coefficient of
`x` to both sides

`\left(-\frac92\right)^2=(81)/(4)`

Completing the square:

Rewrite
`x^2-9x+2=0` in the form
`y=(x-b)^2 +c`

Add the square of half of the coefficient of
`x` to both sides:

`\implies x^2-9x+2+\left(-\frac92\right)^2=\left(-\frac92\right)^2`

`\implies x^2-9x+2+(81)/(4)=(81)/(4)`

`\implies\left(x-\frac92\right)^2 +2=(81)/(4)`

`\implies\left(x-\frac92\right)^2 +2-(81)/(4)=0`

`\implies\left(x-\frac92\right)^2 -(73)/(4)=0`

`\implies\left(x-\frac92\right)^2 -(73)/(4)=0`