Question

Solve the following quadratic equation using the perfect square trinomial pattern x^2 + 10x + 25 = 0

Answer 1

To solve the quadratic equation \( x^2 + 10x + 25 = 0 \) using the perfect square trinomial pattern, we first recognize that the left-hand side can be expressed as a square of a binomial.

The expression \( x^2 + 10x + 25 \) is a perfect square trinomial because it can be rewritten as:

\[
(x + 5)^2 = 0
\]

Now, we set this equation to zero:

\[
(x + 5)^2 = 0
\]

To solve for \( x \), we take the square root of both sides:

\[
x + 5 = 0
\]

Subtracting 5 from both sides, we find:

\[
x = -5
\]

Thus, the solution to the equation \( x^2 + 10x + 25 = 0 \) is

\[
\boxed{-5}
\]

Since this is a perfect square, it has only one solution (a double root).