Find the solution(s) using the quadratic formula.
$4x^2-4x+1=0$

• A. $x=\frac{1}{2}$
• B. $x=-\frac{1}{2}$
• C. $x=1,x=\frac{1}{2}$
• D. $x=1,x=-\frac{1}{2}$

Answer: (A)

Verified step by step guidance

1. Identify the coefficients from the quadratic equation \$4x^2 - 4x + 1 = 0\(. Here, \)a = 4\(, \)b = -4\(, and \)c = 1$.
2. Write down the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).
3. Substitute the values of \(a\), \(b\), and \(c\) into the formula: \(x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4 \cdot 4 \cdot 1}}{2 \cdot 4}\).
4. Simplify inside the square root (the discriminant): calculate \(b^2 - 4ac = (-4)^2 - 4 \cdot 4 \cdot 1\).
5. Evaluate the entire expression step-by-step: first simplify the numerator and denominator separately, then simplify the square root, and finally write the two possible solutions for \(x\) using the \(\pm\) sign.