Question

Solve the equation by completing the square method:
$x^2-10x+9=0$

Answer 1

Given: $x^2-10x+9=0$

Step I: If the coefficient of $x^2$ is $1$, we divide the coefficient of $x$ by $2$

$\Rightarrow$ Coefficient of $x$ $=10$

$\Rightarrow \frac{10}{2}=5$

Step II: Add and subtract the square of result so obtained in Step I.

$\Rightarrow x^2-10x+9+25-25=0$

$\Rightarrow (x^2-10x+25)+9-25=0$

$\Rightarrow (x-5{)}^2-16=0$ [Using $(a-b{)}^2=a^2+b^2-2ab$]

$\Rightarrow (x-5{)}^2=16$

$\Rightarrow x-5=\pm 4$

If $x-5=4$

$\Rightarrow x=9$

If $x-5=-4$

$\Rightarrow x=1$

Therefore, $x=1,9$