Question

Which method would be best to solve
9d^2-100=0
Why?

Answer 1

To solve the equation \( 9d^2 - 100 = 0 \), the best method is to use the **quadratic formula** or recognize it as a difference of squares.

### Here's why:

1. **Structure of the Equation**: The equation is in the standard form of a quadratic equation \( ax^2 + bx + c = 0 \) where \( a = 9 \), \( b = 0 \), and \( c = -100 \).

2. **Difference of Squares**: The equation can also be rearranged to show that it’s a difference of squares:
\[
9d^2 - 100 = 0
\]
can be factored as:
\[
(3d - 10)(3d + 10) = 0
\]
This method is effective because it allows us to equate each factor to zero and solve for \( d \).

### Steps to Solve:

1. **Factoring**:
\[
(3d - 10)(3d + 10) = 0
\]

2. **Set Each Factor to Zero**:
\[
3d - 10 = 0 \quad \text{or} \quad 3d + 10 = 0
\]

3. **Solve for \( d \)**:
- For \( 3d - 10 = 0 \):
\[
3d = 10 \implies d = \frac{10}{3}
\]
- For \( 3d + 10 = 0 \):
\[
3d = -10 \implies d = -\frac{10}{3}
\]

### Conclusion:

The solutions are:
\[
d = \frac{10}{3} \quad \text{and} \quad d = -\frac{10}{3}
\]

Using the difference of squares method is often quicker than applying the quadratic formula, especially when the quadratic can be factored easily as in this case.