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

Question

Solve the following equation:

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

00:00 Find X

00:04 Let's identify the coefficients

00:17 Let's use the roots formula

00:46 Let's substitute appropriate values according to the given data and solve

01:13 Let's calculate the square and products

01:24 The root of 0 is always equal to 0

01:29 When the root equals 0, there is only one solution to the equation

01:51 And this is the solution to the question

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.

$x=-5$