Question

Solve the following quadratic equation using the perfect square trinomial pattern: x2+10x+25=0.(1 point)
x=

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 factored.

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

\[
(x + 5)^2
\]

So, we can rewrite the equation as:

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

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

\[
x + 5 = 0
\]

Now, isolate \( x \):

\[
x = -5
\]

Thus, the solution is:

\[
x = -5
\]