Question

Solve the following quadratic equation using the perfect square trinomial pattern: x^2+10x+25=0
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Answer 1

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

The equation can be rewritten as:

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

This is because:

\[
(x + 5)(x + 5) = x^2 + 5x + 5x + 25 = x^2 + 10x + 25
\]

Now, we can set the expression equal to zero:

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

Next, we take the square root of both sides:

\[
x + 5 = 0
\]

Now, we solve for \( x \):

\[
x = -5
\]

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

\[
\boxed{-5}
\]