Solve the following equation. \( 16 x^{2}+25=40 \mathrm{x} \) Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The solution(s) is/are \( x=\square \) (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no real solutions.

We start with the equation: \[ 16x^2 + 25 = 40x \] **Step 1:** Rearrange the equation to set it equal to zero. \[ 16x^2 - 40x + 25 = 0 \] **Step 2:** Identify the coefficients \( a = 16 \), \( b = -40 \), and \( c = 25 \). **Step 3:** Compute the discriminant. \[ \Delta = b^2 - 4ac = (-40)^2 - 4(16)(25) = 1600 - 1600 = 0 \] **Step 4:** Since the discriminant is 0, there is one real solution (a repeated root). Use the formula: \[ x = \frac{-b}{2a} \] Substitute the values of \( b \) and \( a \): \[ x = \frac{-(-40)}{2(16)} = \frac{40}{32} = \frac{5}{4} \] Thus, the solution is: \[ x = \frac{5}{4} \]