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"?

Question

asked Dec 21, 2023 71.2k views

1 Answer

Bobharley · Answer 1 · 2023-12-27T22:07:16+0000

Answer:

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

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

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

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

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

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