DETAILS MYNOTES OSCOLALG1 2.5.274. Solve the quadratic equation by using the quadratic formula. (Enter your answers as a comma-separated list. \( 4=\square x^{2}-9 x+4=0 \) Submil Answer

To solve the quadratic equation \( 4 = x^2 - 9x + 4 \), we first rearrange it into standard form: \[ x^2 - 9x + 4 - 4 = 0 \] This simplifies to: \[ x^2 - 9x = 0 \] Now, we can apply the quadratic formula, which is given by: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] In our equation \( x^2 - 9x + 0 = 0 \), we have: - \( a = 1 \) - \( b = -9 \) - \( c = 0 \) Now, we can calculate the discriminant \( b^2 - 4ac \): \[ b^2 - 4ac = (-9)^2 - 4(1)(0) = 81 - 0 = 81 \] Now we can substitute \( a \), \( b \), and the discriminant into the quadratic formula: \[ x = \frac{-(-9) \pm \sqrt{81}}{2(1)} = \frac{9 \pm 9}{2} \] This gives us two possible solutions: 1. \( x = \frac{9 + 9}{2} = \frac{18}{2} = 9 \) 2. \( x = \frac{9 - 9}{2} = \frac{0}{2} = 0 \) Thus, the solutions to the equation are: \[ x = 9, 0 \] So, the final answer is: \[ \boxed{9, 0} \]