Solve the equation: x^2-16x+126

The only possible value for x is 7.

Step-by-step explanation:

Recognize that we are given two different equations for the area, A:

1) A = 63 in^2, and

2) A = x^2 - 16x + 126

These two equations must be equal to each other:  A = A

and therefore,

x^2 - 16x + 126 = 63, which becomes x^2 - 16x + 63 = 0 if we subtract 63 from both sides.

Let's solve this using "completing the square."  Take half of the coefficient of x (which coefficient is -16), halve it (obtaining -8) and square the result (obtaining 64).  Now, between -16x and +63 (see the last equation, above), we write +64 - 64, obtaining:

x^2 - 16x + 64 - 64 + 63, which can be rewritten as:

(x - 8)^2 -1 = 0.  Note that this has the form (x - h)^2 + k, and that h is 8 and k is -1.  Thus, the associated parabolic graph has its vertex at (h, k), or (8, -1).  This graph opens up.  Because the vertex is below the x-axis, we know that the graph intersects the x-axis in two places.

Let's find these x values.  Rewrite (x - 8)^2 -1 = 0 as (x - 8)^2 = 1.  Squaring both sides results in x - 8 = 1, which simplifies to x = 9.  This x = 9 is 1 greater than the x-coordinate of the vertex (8).  Knowing tht the graph is symmetrical about the vertical line x = 8, we can safely assume that x = 7 is the other solution, as it is 1 unit to the left of x = 8.

Now we must check these possible solutions {7, 9}.  

Evaluate the second equation at each 7 and 9 and determine whether the area turns out to be 63 in^2, as it must.

(7)^2 - 16(7) + 126 = 49 + 126 - 112, which in turn is equal to 63.  Yes, x = 7 is a possible value for x.

Next:  x = 9.  (9)^2 - 16(9) + 126 = 81 - 112 + 126 = 95.  This does not agree with A = 63 in^2, so we must reject x = 9.

The only possible value for x is 7.

step-by-step explanation:

if x = 2 you have to find x to finish the problem

30 feet

step-by-step explanation:

that would be 2 1/2 * 12

= 24 + 6

= 30 feet   (answer)