To complete the square for the quadratic equation [tex]\( x^2 + 7x = 4 \)[/tex], follow these step-by-step instructions:
1. Identify the coefficient of the linear term (the term with [tex]\( x \)[/tex]):
- The coefficient of [tex]\( x \)[/tex] in [tex]\( x^2 + 7x \)[/tex] is 7.
2. Divide the linear coefficient by 2:
- [tex]\(\frac{7}{2}\)[/tex].
3. Square the result of the division:
- [tex]\(\left(\frac{7}{2}\right)^2 = \left(\frac{7}{2}\right) \times \left(\frac{7}{2}\right) = \frac{49}{4}\)[/tex].
To match the numerical result provided earlier:
- [tex]\(\left(\frac{7}{2}\right)^2 = 12.25\)[/tex]
So, the number you would add to both sides of [tex]\( x^2 + 7x = 4 \)[/tex] to complete the square is:
- [tex]\(\left(\frac{7}{2}\right)^2\)[/tex].
Hence, the correct option is:
- [tex]\(\left(\frac{7}{2}\right)^2\)[/tex].
