To solve the equation:

$1 = a((-2) - (-3))^2 + 3$

1. Simplify the expression inside the parentheses: $(-2) - (-3) = -2 + 3 = 1$

2. Substitute back into the equation: $1 = a(1)^2 + 3$

3. Since $1^2 = 1$, we have: $1 = a \cdot 1 + 3$ $1 = a + 3$

4. Solve for $a$: $a = 1 - 3 = -2$

So, the solution is: $a = -2$

Would you like more details, or do you have any questions?

Related Questions

1. How would the solution change if we had $1 = a((-2) - (-4))^2 + 3$?
2. What if the equation were $2 = a((-2) - (-3))^2 + 4$?
3. How would we solve if the exponent was 3 instead of 2?
4. What happens if $a$ is squared in the equation?
5. How can we verify if $a = -2$ is correct by substituting back?

Tip

Always simplify inside the parentheses first before dealing with powers or multipliers.