To solve the quadratic equation \( 4a^2 + 25 = 20a \), follow these steps:

### Step 1: Rearrange the equation
First, we want to rearrange the equation to have all terms on one side, setting the equation equal to zero:
\[
4a^2 - 20a + 25 = 0
\]

### Step 2: Simplify the equation (if possible)
In this case, the equation is already simplified.

### Step 3: Solve using the quadratic formula
The quadratic formula is given by:
\[
a = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
For the equation \( 4a^2 - 20a + 25 = 0 \), the coefficients are:
- \( a = 4 \)
- \( b = -20 \)
- \( c = 25 \)

Substituting these values into the quadratic formula:

\[
a = \frac{-(-20) \pm \sqrt{(-20)^2 - 4(4)(25)}}{2(4)}
\]

### Step 4: Calculate the discriminant
\[
a = \frac{20 \pm \sqrt{400 - 400}}{8}
\]
\[
a = \frac{20 \pm \sqrt{0}}{8}
\]

### Step 5: Solve for \( a \)
Since the discriminant is 0, there is only one solution:
\[
a = \frac{20 \pm 0}{8} = \frac{20}{8} = 2.5
\]

Thus, the solution is \( a = 2.5 \).

Would you like any more details or have any questions? Here are some related questions:

1. What is the significance of the discriminant in the quadratic formula?
2. How do you factor a quadratic equation like this one?
3. Can quadratic equations have complex solutions?
4. What are the different methods to solve quadratic equations?
5. How does the quadratic formula work for different types of quadratic equations?

**Tip:** When using the quadratic formula, the discriminant (the part under the square root) tells you how many solutions the equation has: 0 (one solution), positive (two solutions), or negative (no real solutions, but two complex ones).

Learn how to solve the quadratic equation 4a^2 + 25 = 20a with a detailed step-by-step solution. This problem involves rearranging equations and applying the quadratic formula. Suitable for high school students.

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