Question

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

Answer 1

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

The expression \( x^2 + 10x + 25 \) can be rewritten as:

\[
(x + 5)^2
\]

Now, we can rewrite the equation as:

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

Next, we take the square root of both sides:

\[
x + 5 = 0
\]

Solving for \( x \), we subtract 5 from both sides:

\[
x = -5
\]

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

\[
\boxed{-5}
\]