Answer :
Answer: [tex]x^2+\frac{1}{2}x+\frac{1}{16}=2 +\frac{1}{16}[/tex]
Step-by-step explanation:
Given the following Quadratic equation:
[tex]x^2+\frac{1}{2}x=2 +[/tex]
You can change its formed by Completing the square.
In order to do Complete the square, you can follow these steps:
1. You can identify that:
[tex]b=\frac{1}{2}[/tex]
2. Then, you can find [tex](\frac{b}{2})^2[/tex]. This is:
[tex](\frac{\frac{1}{2}}{2})^2=(\frac{1}{4})^2=\frac{1}{16}[/tex]
3. Now you must add [tex]\frac{1}{16}[/tex] to both sides of the Quadratic equation in order to keep the balance. Then:
[tex]x^2+\frac{1}{2}x+\frac{1}{16}=2 +\frac{1}{16}[/tex]
4. Finally, simplifying by actoring and adding the like terms, you get:
[tex](x+\frac{1}{4})^2=\frac{9}{4}[/tex]