Factor the perfect-square trinomial on the left side of the equation. (x+1/4 surd )^2=(4)/(9) Apply the square root property of equality. x+1/4v=pm

To solve the equation \((x + \frac{1}{4})^2 = \frac{4}{9}\), we will follow these steps:<br /><br />1. **Apply the square root property of equality**:<br /> \[<br /> \sqrt{(x + \frac{1}{4})^2} = \pm \sqrt{\frac{4}{9}}<br /> \]<br /><br />2. **Simplify the square roots**:<br /> \[<br /> x + \frac{1}{4} = \pm \frac{2}{3}<br /> \]<br /><br />3. **Solve for \(x\)**:<br /> \[<br /> x + \frac{1}{4} = \frac{2}{3} \quad \text{or} \quad x + \frac{1}{4} = -\frac{2}{3}<br /> \]<br /><br />4. **Isolate \(x\)**:<br /> \[<br /> x = \frac{2}{3} - \frac{1}{4} \quad \text{or} \quad x = -\frac{2}{3} - \frac{1}{4}<br /> \]<br /><br />5. **Find a common denominator and simplify**:<br /> \[<br /> x = \frac{8}{12} - \frac{3}{12} = \frac{5}{12} \quad \text{or} \quad x = -\frac{8}{12} - \frac{3}{12} = -\frac{11}{12}<br /> \]<br /><br />So, the solutions to the equation are:<br />\[<br />x = \frac{5}{12} \quad \text{or} \quad x = -\frac{11}{12}<br />\]