Factor the expression a^2+a+-1

 Exercise

$a^2+a-1$

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Add and subtract $\displaystyle\left(\frac{b}{2a}\right)^2$

$a^2+a-1+\frac{1}{4}-\frac{1}{4}$

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Factor the perfect square trinomial $a^2+a+\frac{1}{4}$

$\left(a+\sqrt{\frac{1}{4}}\right)^2-1-\frac{1}{4}$

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Calculate the power $\sqrt{\frac{1}{4}}$

$\left(a+\frac{1}{2}\right)^2-1-\frac{1}{4}$

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Simplify the addition $\left(a+\frac{1}{2}\right)^2-1-\frac{1}{4}$

$\left(a+\frac{1}{2}\right)^2+\frac{-1-4}{4}$

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Subtract the values $-1$ and $-4$

$\left(a+\frac{1}{2}\right)^2-\frac{5}{4}$

$\left(a+\frac{1}{2}\right)^2-\frac{5}{4}$

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