DETAILS MY NOTES LARAT11 1.4.038. O/6 Submissiont Used \[ 4 x^{2}-4 x=1 \] \[ x= \]

To solve the equation \(4x^2 - 4x - 1 = 0\), we can use the quadratic formula, which states that for any quadratic equation in the form \(ax^2 + bx + c = 0\), the solutions for \(x\) are given by: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] In this case, \(a = 4\), \(b = -4\), and \(c = -1\). Plug in these values to find \(x\). When you work through this, you’ll discover the roots are complex yet fascinating! Make sure you calculate the discriminant (the part under the square root) correctly, as this will inform you whether the solution is real or imaginary. Now, for common mistakes: students often forget to simplify the final answer or miscalculate the discriminant. Double-check your arithmetic, especially when squares and negatives get involved! And remember, taking it slow means fewer mistakes!