Answer:
[tex](x-\frac{1}{4})^{2} \geq \frac{-39}{16}[/tex]
Step-by-step explanation:
Rewrite into standard form:
[tex]2x^{2} -x+5 \geq 0[/tex]
Complete the square:
[tex]2(x-\frac{1}{4} )^{2} + \frac{39}{8} \geq 0[/tex]
Subtract [tex]\frac{39}{8}[/tex] from both sides:
[tex]2(x-\frac{1}{4})^{2} \geq \frac{-39}{8}[/tex]
Divide both sides by 2:
[tex](x-\frac{1}{4})^{2} \geq \frac{-39}{\frac{8}{2}}[/tex]
Simplify:
[tex](x-\frac{1}{4})^{2} \geq \frac{-39}{16}[/tex]
