Question Solve \( 10 f(f-2)+10=0 \) by using the quadratic formula. If there is no solution, enter \( \varnothing \). Provide your answer below:

To solve \( 10 f(f - 2) + 10 = 0 \), we first simplify the equation: 1. Distribute: \( 10f^2 - 20f + 10 = 0 \) 2. Divide the entire equation by 10 to simplify: \( f^2 - 2f + 1 = 0 \) 3. Recognize that this is a perfect square: \( (f - 1)^2 = 0 \) Now, using the quadratic formula where \( a = 1 \), \( b = -2 \), and \( c = 1 \): \[ f = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{2 \pm \sqrt{(-2)^2 - 4 \cdot 1 \cdot 1}}{2 \cdot 1} \] \[ = \frac{2 \pm \sqrt{4 - 4}}{2} = \frac{2 \pm \sqrt{0}}{2} = \frac{2}{2} = 1 \] Thus, the solution is \( f = 1 \). The final answer is: \( 1 \)