You notice that the following problem 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? x2 −8x + c = 13 (1 point) Responses 64 64 -4 -4 4 4 16 16 -8
To complete the square for the equation x^2 - 8x + c = 13, we first need to write it in the form of a perfect square trinomial.
To do this, we have to take half of the coefficient of x, square it, and add it to both sides of the equation to maintain balance.
In this case, half of the coefficient of x is -8/2 = -4. Squaring this gives us (-4)^2 = 16.
Adding 16 to both sides of the equation, we get:
x^2 - 8x + 16 = 13 + 16
x^2 - 8x + 16 = 29
Now, the left-hand side is a perfect square trinomial: (x - 4)^2 = 29
Therefore, the value of c that would make the left-hand side of this equation a perfect square trinomial is 16.