Solve the following: (x-1 2 )^2=4 - Vidyadip

Question

Solve the following: $\left(x-\frac{1}{2}\right)^2=4$

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Answer

$\left( x -\frac{1}{2}\right)^2=4$
$x^2-x+\frac{1}{4}=4$
$x^2-x-\frac{15}{4}=0$
$x^2+\frac{3}{2} x-\frac{5}{2} x-\frac{15}{4}=0$
$ x \left( x +\frac{3}{2}\right)-\frac{5}{2}\left( x +\frac{3}{2}\right)=0 $
$ \left( x +\frac{3}{2}\right)\left( x -\frac{5}{2}\right)=0$
$x =-\frac{3}{2}, x =\frac{5}{2}$

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