[tex]x^2+x= \frac{7}{4}[/tex]
Take one-half of the coefficient of x and square it, then add it to both sides.
[tex]x^2+x+ (\frac{1}{4}) =\frac{7}{4}+ (\frac{1}{4}) [/tex]
[tex]x^2+x+(\frac{1}{4})= 2 [/tex]
[tex]\left(x+\frac{1}{2}\right)^2=2[/tex]
[tex]x+\frac{1}{2}=\pm \sqrt{2}[/tex]
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[tex]x+\frac{1}{2}=- \sqrt{2}[/tex]
[tex]x=-\frac{1}{2}- \sqrt{2}[/tex] <=
AND
[tex]x+\frac{1}{2}= \sqrt{2}[/tex]
[tex]x= \sqrt{2}-\frac{1}{2}[/tex] <=
