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To complete the square with the following algebraic expression, what should the third term of the trinomial be?

x2+5/3x+_?

ManuelBautista2019  Feb 28, 2018

#1
+19054
+1

To complete the square with the following algebraic expression, what should the third term of the trinomial be?

x2+5/3x+_?

I asume: $$x^2+\frac{5}{3}x +\ ? =$$

$$\begin{array}{|rcll|} \hline (x+a)^2 &=& x^2+\underbrace{2a}_{=\frac53}x+a^2 \\ && 2a = \frac53 \\ && a = \frac{5}{6} \\ && a^2 = \frac{5^2}{6^2} \\ && = \frac{25}{36} \\ \hline \end{array}$$

The third term of the trinomial is $$\mathbf{\frac{25}{36}}$$

heureka  Feb 28, 2018
Sort:

#1
+19054
+1

To complete the square with the following algebraic expression, what should the third term of the trinomial be?

x2+5/3x+_?

I asume: $$x^2+\frac{5}{3}x +\ ? =$$

$$\begin{array}{|rcll|} \hline (x+a)^2 &=& x^2+\underbrace{2a}_{=\frac53}x+a^2 \\ && 2a = \frac53 \\ && a = \frac{5}{6} \\ && a^2 = \frac{5^2}{6^2} \\ && = \frac{25}{36} \\ \hline \end{array}$$

The third term of the trinomial is $$\mathbf{\frac{25}{36}}$$

heureka  Feb 28, 2018
#2
+12117
0