Solve the Quadratic Equation: x²+10x+25=0 Step-by-Step

Solve the following equation:

$x^2+10x+25=0$

The given quadratic equation is $x^2 + 10x + 25 = 0$.

Notice that $x^2 + 10x + 25$ is a perfect square trinomial, which can be factored as $(x + 5)^2$. Let's verify by expanding:

$(x + 5)^2 = (x + 5)(x + 5) = x^2 + 5x + 5x + 25 = x^2 + 10x + 25$.

Since the factoring is correct, we rewrite the equation:

$(x + 5)^2 = 0$.

Take the square root of both sides:

$x + 5 = 0$.

Solving for $x$, we find:

$x = -5$.

The equation has a double root, meaning the solution is repeated. Thus, the final solution is:

$x = -5$.

This matches the given correct answer.