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.
-
Identify the perfect square trinomial: \[ x^2 + 10x + 25 = (x + 5)^2 \]
-
Rewrite the equation using the factored form: \[ (x + 5)^2 = 0 \]
-
Take the square root of both sides: \[ x + 5 = 0 \]
-
Solve for \( x \): \[ x = -5 \]
Thus, the solution to the equation \( x^2 + 10x + 25 = 0 \) is: \[ \boxed{-5} \]
1 answer