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?
x^2 - 8x + c = 13
To complete the square, we need to find the value of c that would turn x^2 - 8x + c into a perfect square trinomial.
In a perfect square trinomial of the form (x - a)^2, the constant term is the square of half the coefficient of the x-term. So in this case, we want our perfect square trinomial to be (x - 4)^2.
This means that c should be equal to (half of -8)^2, because we want c to make x^2 - 8x + c = (x - 4)^2.
(-8 / 2)^2 = (-4)^2 = 16
So, the value of x that would make the left-hand side of the equation a perfect square trinomial is 16.