Solving Quadratic Equations Using Patterns Practice

Question

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Question
Solve the following quadratic equation using the perfect square trinomial pattern: x2+10x+25=0
.(1 point)
x=
Remaining Attempts : 3

Answer 1

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

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

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

\[ x + 5 = 0 \]

Now, isolate \(x\) by subtracting 5 from both sides:

\[ x = -5 \]

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

\[ \boxed{-5} \]