Help with the following complete the square equation...

Why do this?

Because we want to be able to factor the left hand side into the form p^2, where p is some algebraic expression. This will help us ultimately solve for x.

Currently, the left hand side is x^2+16x which does factor to x(x+16), but that isn't in the form p^2. We want something like (x+1)^2 or (x+2)^2. The general form is (x+k)^2 where k is some fixed constant.

Let's expand out (x+k)^2 using the FOIL rule and we get x^2+2kx+k^2

The x coefficient is 2k. If we cut that in half, we get k. Squaring that result leads to k^2.

So we have this order: 2k cuts in half to k then square it to get k^2

For x^2+16x, we have the x coefficient as 16. That cuts in half to 8, then that squares to 64. We add 64 to both sides

Note how

x^2+16x = 9

x^2 + 16x + 64 = 9+64

(x+8)^2 = 73

From here, we apply the square root to both sides and then subtract 8 from both sides to fully isolate x. You would get two different solutions.

I recommend you use the FOIL rule to confirm that (x+8)^2 expands out to x^2+16x+64, to help check your work.

step-by-step explanation:

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,