\( 361 h^{2}+38 h+1=0 \) Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. \( h=\square \) Submit

To solve the quadratic equation \( 361 h^{2}+38 h+1=0 \), we can use the quadratic formula \( h = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 361 \), \( b = 38 \), and \( c = 1 \). First, we calculate the discriminant: \[ b^2 - 4ac = 38^2 - 4 \times 361 \times 1 = 1444 - 1444 = 0 \] Since the discriminant is zero, there is one real solution. Now applying the quadratic formula: \[ h = \frac{-38 \pm \sqrt{0}}{2 \times 361} = \frac{-38}{722} = -\frac{19}{361} \] So the solution is \( h = -\frac{19}{361} \). \( h = -\frac{19}{361} \)