Final answer:
Finding the value of x using completing the square requires a quadratic equation representing the area in terms of x. Without the specific quadratic equation, we cannot apply the method or provide a numerical answer.
Step-by-step explanation:
To find the value of x when given that the area of the triangle is 54, and you are instructed to use the method of completing the square, you need to set up the quadratic equation that represents the area of the triangle. For instance, if the base and height of the triangle can be expressed in terms of x, the area would then be expressed as 0.5 * base * height. However, it seems there might be some missing information from the question as we do not have an explicit expression for the area in terms of x.
If we were given a quadratic equation, let's say, in the form ax^2 + bx + c = 54, we would rearrange it into the standard form ax^2 + bx + (c - 54) = 0 before using the completing the square method. This involves dividing the entire equation by a (if a is not 1), then moving the constant term to the other side of the equation, and finding a value to add to both sides such that the left side becomes a perfect square trinomial. Finally, you would take the square root of both sides and solve for x.
In contrast to the typical approach of using the quadratic formula, completing the square provides a more straightforward solution when the quadratic can be easily converted to a perfect square trinomial. However, without the specific quadratic equation for this problem, we cannot demonstrate the complete method here.