\[3{x}^{2}+7x\]
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Formula
1
The expression 3x2+7x3{x}^{2}+7x fits the form ax2+bx+ca{x}^{2}+bx+c. Let's complete the square, where:
a=3b=7c=0\begin{aligned}&a=3\\&b=7\\&c=0\end{aligned}

2
Factor out aa, which is 33.
3(x2+73x)3({x}^{2}+\frac{7}{3}x)

3
Introduce the constant kk, which is 4936\frac{49}{36} in our case.
3(x2+73x+4936−4936)3({x}^{2}+\frac{7}{3}x+\frac{49}{36}-\frac{49}{36})

4
Use Square of Sum: (a+b)2=a2+2ab+b2{(a+b)}^{2}={a}^{2}+2ab+{b}^{2}.
3((x+76)2−4936)3({(x+\frac{7}{6})}^{2}-\frac{49}{36})

5
Expand.
3(x+76)2−49123{(x+\frac{7}{6})}^{2}-\frac{49}{12}

Done
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