Question

fill in the blanks so the left side is a perfect square trinomial

Answer 1

We need to complete the perfect square. A perfect square has the following form:

$a^2\cdot x^2+2\cdot a\cdot b\cdot x+b^2=(a\cdot x+b)^2$

In our case we have:

$x^2-8x+\cdots$

We can immediately deterine the value of "a", which is the root of number multiplying x², since this number is 1, then:

$a=1$

This also means we can find "b", because the second term is equal to the product of 2, a, and b. So we have:

$\begin{gathered} b=\frac{8}{2} \\ b=4 \end{gathered}$

With this we can determine the blank, because it is b². So we have:

$\begin{gathered} x^2-8x+4^2 \\ x^2-8x+16=(x-4)^2 \end{gathered}$

The first missing space is 16 and the second is 4.