Solve Quadratic Equation: 36x² - 144x + 144 = 0 Step-by-Step

To solve the quadratic equation $36x^2 - 144x + 144 = 0$, we first examine its structure to determine the best method for solution:

Step 1: Simplify the equation.
Notice that each term in the equation $36x^2 - 144x + 144$ is divisible by 36. Let's simplify it by dividing each term by 36:

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

Step 2: Factor the simplified equation.
The equation $x^2 - 4x + 4$ can be factored as $(x - 2)^2 = 0$, since both 2 and -2 added yield -4, and multiplied give 4.

Step 3: Solve for x.
Given $(x - 2)^2 = 0$, the solution is $x - 2 = 0$, which results in:

$x = 2$

Therefore, the solution to the equation is $x = 2$.

This corresponds to the provided correct answer choice $x=2$.