Evaluate
\frac{1}{4}-6x-x^{2}
Expand
\frac{1}{4}-6x-x^{2}
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-6x+\left(\frac{1}{2}\right)^{2}-x^{2}
Consider \left(\frac{1}{2}-x\right)\left(\frac{1}{2}+x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
-6x+\frac{1}{4}-x^{2}
Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.
-6x+\left(\frac{1}{2}\right)^{2}-x^{2}
Consider \left(\frac{1}{2}-x\right)\left(\frac{1}{2}+x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
-6x+\frac{1}{4}-x^{2}
Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.
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