Question

How do you solve $x^2-6x=16$ by completing the square?

Answer 1

Solve the given equation:

Given that $x^2-6x=16$

To complete the square, add square of ($\frac{1}{2}$ of co-efficient of $x$) to both sides i.e. ${\left(\frac{-6}{2}\right)}^2=9$

$\Rightarrow$$x^2+2(-3)x+9=16+9$

$\Rightarrow$ ${(x-3)}^2=25$

Take the square root of both sides,

$\Rightarrow$$\sqrt{{(x-3)}^2}=\sqrt{25}$

$\Rightarrow$ $x-3=\pm 5$

$\Rightarrow$ $x=3\pm 5$

$\Rightarrow$ $x=3-5orx=3+5$

$\Rightarrow$ $x=-2orx=8$

Hence, the solution of the given equation is $x=-2orx=8$.