Solve Quadratic Equation: x² - 4x + 4 = 0 Step-by-Step

Solve the following equation:

$x^2-4x+4=0$

The given equation is:

$x^2 - 4x + 4 = 0$

This resembles a perfect square trinomial. The expression $x^2 - 4x + 4$ can be rewritten as $(x-2)^2$. This can be verified by expanding $(x-2)(x-2)$ to confirm it equals $x^2 - 4x + 4$.

Therefore, the equation becomes:

$(x-2)^2 = 0$

To solve for $x$, take the square root of both sides:

$x - 2 = 0$

Adding 2 to both sides gives:

$x = 2$

Thus, the solution to the equation $x^2 - 4x + 4 = 0$ is $x = 2$, which corresponds to the unique real root of the equation.