To solve the equation $x^2 + 10x + 25 = 0$, we can use the method of factoring, as this is a perfect square trinomial.

Step-by-Step Solution:

1. Identify the form of the trinomial: The equation is in the form $x^2 + 2 \cdot 5 \cdot x + 5^2 = 0$, which resembles the perfect square $(x + 5)^2$.

2. Rewrite the equation: $x^2 + 10x + 25 = (x + 5)^2$

3. Set the factored expression equal to zero: $(x + 5)^2 = 0$

4. Solve for $x$: Take the square root of both sides to isolate $x$: $x + 5 = 0$ $x = -5$

Final Answer:

The solution is $x = -5$.

Would you like more details on factoring or have any questions?

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Further Practice Questions:

1. Solve $x^2 + 12x + 36 = 0$.
2. Solve $x^2 - 14x + 49 = 0$.
3. Factor and solve $x^2 + 6x + 9 = 0$.
4. Use the quadratic formula to solve $x^2 + 10x + 25 = 0$ and confirm the solution.
5. Solve $x^2 + 8x + 16 = 0$ by factoring.

Tip: When solving quadratic equations, check if the equation can be factored as a perfect square—it often simplifies the process.