You notice that the following problem cannot be factored so you solve it by completing the square. What value of x would make the left - hand side of this equation a perfect square trinomial?

Question

x^2 - 8x + c = 13

a. 16

b. 4

c. 64

d.-8

f. -4

Answer 1

To make the left-hand side of the equation a perfect square trinomial, we need to find the value of c that will satisfy the equation when completing the square.

To complete the square, we look at the coefficient of x, which is -8, and take half of it: (-8/2)^2 = 16

So, c = 16

Now, we add 16 to both sides of the equation:

x^2 - 8x + 16 = 13 + 16
(x - 4)^2 = 29

Now, we can see that the left-hand side is a perfect square trinomial when x = 4.

Therefore, the answer is:

b. 4