Solve the given quadratic equation using the square root property. $\(\left\)(x-\(\frac\)12\(\right\))^2-5=0$

• A. $x=\(\frac\)12+\(\sqrt\)5,x=\(\frac\)12-\(\sqrt\)5$
• B. $x=\(\frac\)52,x=-\(\frac\)52$
• C. $x=\(\frac{\sqrt5}{2}\),x=-\(\frac{\sqrt5}{2}\)$
• D. $x=\(\frac\)12,x=-\(\frac\)12$

Answer: (A)

Verified step by step guidance

1. Start by isolating the squared term. The given equation is \((x - \frac{1}{2})^2 - 5 = 0\). Add 5 to both sides to get \((x - \frac{1}{2})^2 = 5\).
2. Apply the square root property, which states that if \(a^2 = b\), then \(a = \pm \sqrt{b}\). Here, set \(x - \frac{1}{2} = \pm \sqrt{5}\).
3. Solve for \(x\) by adding \(\frac{1}{2}\) to both sides of the equation. This gives \(x = \frac{1}{2} + \sqrt{5}\) and \(x = \frac{1}{2} - \sqrt{5}\).
4. These two expressions represent the solutions to the quadratic equation. The solutions are \(x = \frac{1}{2} + \sqrt{5}\) and \(x = \frac{1}{2} - \sqrt{5}\).
5. Verify the solutions by substituting them back into the original equation to ensure they satisfy \((x - \frac{1}{2})^2 - 5 = 0\).