Solve the following quadratic equation using the perfect square trinomial pattern: x2+10x+25=0

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1 answer

To solve the quadratic equation \(x^2 + 10x + 25 = 0\) using the perfect square trinomial pattern, we first recognize that this expression can be factored.

The perfect square trinomial can be expressed in the form \((x + a)^2\), where \(a\) is a number.

In this case, we notice that:

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

This is because \(5^2 = 25\) and \(2 \cdot 5 = 10\).

Now our equation becomes:

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

Next, we can take the square root of both sides:

\[ x + 5 = 0 \]

Subtracting 5 from both sides gives us:

\[ x = -5 \]

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

\[ \boxed{-5} \]