Question
You notice that the following quadratic equation cannot be factored, so you solve it by completing the square.
What value of c would make the left-hand side of this equation a perfect square trinomial?
x^2 − 8x + c = 13
(1 point)
Responses
-8
-8
64
64
16
16
4
4
-4
What value of c would make the left-hand side of this equation a perfect square trinomial?
x^2 − 8x + c = 13
(1 point)
Responses
-8
-8
64
64
16
16
4
4
-4
Answers
GPT-4o mini
To make the left-hand side of the equation \( x^2 - 8x + c \) a perfect square trinomial, we need to complete the square.
The general approach for completing the square is to take the coefficient of \( x \) (which is -8 in this case), divide it by 2, and then square the result.
1. Take the coefficient of \( x \): \(-8\)
2. Divide it by 2: \(-8 / 2 = -4\)
3. Square the result: \((-4)^2 = 16\)
So, the value of \( c \) that would make \( x^2 - 8x + c \) a perfect square trinomial is \( 16 \).
Thus, the answer is \( \boxed{16} \).
The general approach for completing the square is to take the coefficient of \( x \) (which is -8 in this case), divide it by 2, and then square the result.
1. Take the coefficient of \( x \): \(-8\)
2. Divide it by 2: \(-8 / 2 = -4\)
3. Square the result: \((-4)^2 = 16\)
So, the value of \( c \) that would make \( x^2 - 8x + c \) a perfect square trinomial is \( 16 \).
Thus, the answer is \( \boxed{16} \).