Once you have an equation of the form $(x-2)^2 = 144$, what operation undoes squaring? Remember that you should consider both the positive and negative results.

From $|x-2| = 12$, write two simple equations with $x-2$ equal to a positive and a negative number, then solve each for $x$.

After you find both values of $x$, pay attention to the word "positive" in the question to decide which value to choose.

In one line, type y = (x - 2)^2 / 9. In another line, type y = 16 so you have both graphs on the same coordinate plane.

Look for the points where the parabola y = (x - 2)^2 / 9 intersects the horizontal line y = 16. Click on each intersection to see its coordinates.

You will see two intersection points with different x-coordinates. Note both x-values, then select the one that is positive; that is the positive solution to the equation.

Start with the equation:

Multiply both sides by 9 to eliminate the denominator:

Compute $16 \cdot 9$:

To undo the square on $x-2$, take the square root of both sides. Remember that taking a square root gives two possible values, positive and negative:

So you get:

The equation $|x-2| = 12$ means that $x-2$ can be 12 or $-12$:

Solve each equation:

For $x - 2 = 12$:

For $x - 2 = -12$:

The question asks for the positive solution, so the correct answer is $14$.