Answer:
[tex]x=-\frac{7}{6}\\x=\frac{1}{6}[/tex]
Step-by-step explanation:
The equation to solve is:
[tex](x+\frac{1}{2})^2=\frac{4}{9}[/tex]
To get rid of the "square", we need to take square root of both sides:
[tex]\sqrt{(x+\frac{1}{2})^2}=\sqrt{\frac{4}{9}}\\x+\frac{1}{2}=\frac{\sqrt{4}}{\sqrt{9}}[/tex]
Then we use algebra to find the value(s) of x. Remember, when we take square root, we have to add up a "+-" (on the right side). Shown below:
[tex]x+\frac{1}{2}=+-\frac{\sqrt{4}}{\sqrt{9}}\\x+\frac{1}{2}=+-\frac{2}{3}\\x=\frac{2}{3}-\frac{1}{2}=\frac{1}{6}\\x=-\frac{2}{3}-\frac{1}{2}=-\frac{7}{6}[/tex]
So these are 2 answers for x.