Question

Part A: Find the value of c that will result in a perfect square trinomial.

x^2 + 18x + c = 25 + c

Part B: Rewrite the above equation into a perfect square binomial form.
(x + [value])^2 = [value]

A. Part A: c = 7; Part B: (x + 9)^2 = 16
B. Part A: c = 16; Part B: (x + 9)^2 = 7
C. Part A: c = 9; Part B: (x + 18)^2 = 25
D. Part A: c = 25; Part B: (x + 9)^2 =

Answer 1

To find the value of c that will result in a perfect square trinomial, rewrite the equation in the form (x + a)^2 = b. For the given equation x^2 + 18x + c = 25 + c, the value of c is 7 and the equation in perfect square binomial form is (x + 9)^2 = 32.

Step-by-step explanation:

To find the value of c that will result in a perfect square trinomial, we need to rewrite the given equation in the form (x + a)^2 = b.

For the given equation x^2 + 18x + c = 25 + c, we can identify that the coefficient of x is 18. To make it a perfect square trinomial, we take half of the coefficient of x (18/2 = 9) and square it to get the value of a. This gives us (x + 9)^2.

The constant term on the right side of the equation is 25 + c. To make it equal to b (the constant term in the perfect square binomial form), we need to set 25 + c = b. Therefore, the value of c is 7. So, the answer is Part A: c = 7 and Part B: (x + 9)^2 = 25 + c = 25 + 7 = 32.