how to solve this problem. Completing the square. Find the value of a such that u^2-8u+a is a perfect square

To complete the square, you take the middle term (-8), take half of it, and then square it. That's your term for a.

Thank-you Jen

To solve this problem, we need to complete the square for the given quadratic expression u^2 - 8u + a.

To complete the square, we follow these steps:

Step 1: Identify the coefficient of the linear term, which is -8u in this case, and divide it by 2. In this example, -8u/2 = -4u.

Step 2: Square the result from step 1, which gives (-4u)^2 = 16u^2.

Step 3: Add the value obtained in step 2 to both sides of the equation.
u^2 - 8u + a + 16u^2 = a + 16u^2 - 8u + u^2 = (a + 16)u^2 -8u + u^2

Now, we have the equation in the form:
(a + 16)u^2 - 8u + u^2

Step 4: Set this expression equal to a perfect square, c^2.
(a + 16)u^2 - 8u + u^2 = c^2

Step 5: Equate the coefficients of u^2 and u to zero on both sides of the equation.
a + 16 = 0 --(1)
-8u = 0 --(2)
u^2 = c^2 --(3)

From equation (2), we find that u = 0.

From equation (3), we know that u^2 = c^2, which means c can be either positive or negative.

Step 6: Solve equation (1) to find the value of a.
a + 16 = 0
a = -16

Therefore, the value of a that makes the expression u^2 - 8u + a a perfect square is a = -16.