Simplify the inequlaity x^2−x+6>0 for x.
[tex]\begin{gathered} x^2-x+6>0 \\ x^2-2\cdot\frac{1}{2}\cdot x+\frac{1}{4}-\frac{1}{4}+6>0 \\ (x-\frac{1}{2})^2+\frac{23}{4}>0 \\ (x-\frac{1}{2})^2+\frac{23}{4}-\frac{23}{4}>0-\frac{23}{4} \\ (x-\frac{1}{2})^2>-\frac{23}{4} \end{gathered}[/tex]
Since above inequality is true for every value of x. Thus solution of equation is,
[tex](-\infty,\infty)[/tex]
Answer:
[tex](-\infty,\infty)[/tex]
