Solve the Quadratic Equation: X²+4X+4=0 Step-by-Step

Question

Solve for X:

$X^2+4X+4=0$

00:00 Find X

00:03 Note the coefficients, each number is as if multiplied by 1

00:10 Use the roots formula

00:19 Substitute appropriate values according to the given data and solve for X

00:25 Calculate the products and the square

00:35 And this is the solution to the question

To solve the quadratic equation $X^2 + 4X + 4 = 0$ , we can attempt to factor it as a perfect square trinomial.

Step 1: Recognize that the equation is a perfect square trinomial because it can be written as $(X + 2)^2$ . The relationship is $(X + 2)(X + 2) = X^2 + 4X + 4$ .
Step 2: Set the factored equation equal to zero: $(X + 2)^2 = 0$ .
Step 3: Solve for $X$ by setting $X + 2 = 0$ .
Step 4: Solving $X + 2 = 0$ gives $X = -2$ .

Therefore, the solution to the equation is $X = -2$ .

Thus, the correct answer choice is $x = -2$ , corresponding to choice 1.

$x=-2$