Question

Complete the square to solve the equation below

Answer 1

$x^2+x= \frac{7}{4}$

Take one-half of the coefficient of x and square it, then add it to both sides.

$x^2+x+ (\frac{1}{4}) =\frac{7}{4}+ (\frac{1}{4})$

$x^2+x+(\frac{1}{4})= 2$

$\left(x+\frac{1}{2}\right)^2=2$

$x+\frac{1}{2}=\pm \sqrt{2}$
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$x+\frac{1}{2}=- \sqrt{2}$
$x=-\frac{1}{2}- \sqrt{2}$ <=

AND

$x+\frac{1}{2}= \sqrt{2}$
$x= \sqrt{2}-\frac{1}{2}$ <=