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

Answer:

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

$\left(-\dfrac92\right)^2=\dfrac{81}{4}$

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:

$\implies x^2-9x+2+\left(-\dfrac92\right)^2=\left(-\dfrac92\right)^2$

$\implies x^2-9x+2+\dfrac{81}{4}=\dfrac{81}{4}$

$\implies\left(x-\dfrac92\right)^2 +2=\dfrac{81}{4}$

$\implies\left(x-\dfrac92\right)^2 +2-\dfrac{81}{4}=0$

$\implies\left(x-\dfrac92\right)^2 -\dfrac{73}{4}=0$

$\implies\left(x-\dfrac92\right)^2 -\dfrac{73}{4}=0$