Solve for d.

Question

9d2 − 69 = –33

Write your answers as integers or as proper or improper fractions in simplest form.

d =
or d =

Answer 1

To solve the equation \( 9d^2 - 69 = -33 \), we first rearrange it to isolate the \( d^2 \) term.

1. Start by adding 69 to both sides of the equation: \[ 9d^2 - 69 + 69 = -33 + 69 \] \[ 9d^2 = 36 \]

2. Next, divide both sides by 9 to solve for \( d^2 \): \[ d^2 = \frac{36}{9} \] \[ d^2 = 4 \]

3. Now, take the square root of both sides. Remember to consider both the positive and negative roots: \[ d = \pm \sqrt{4} \] \[ d = \pm 2 \]

Therefore, the solutions for \( d \) are: \[ d = 2 \quad \text{or} \quad d = -2 \]