Answer :
group
c(x)=(x²-16x)+84
take 1/2 of -16 and square it
-16/2=-8, (-8)²=64
ad negative and positive inside
c(x)=(x²-16x+64-64)+84
factor
c(x)=((x-8)²-64)+84
distribute or get rid of paenthsees
c(x)=(x-8)²-64+84
add
c(x)=(x-8)²+20
c(x)=(x²-16x)+84
take 1/2 of -16 and square it
-16/2=-8, (-8)²=64
ad negative and positive inside
c(x)=(x²-16x+64-64)+84
factor
c(x)=((x-8)²-64)+84
distribute or get rid of paenthsees
c(x)=(x-8)²-64+84
add
c(x)=(x-8)²+20
Here we need to write a quadratic polynomial in vertex form by completing squares.
We will get: c(x) - 20 = (x - 8)^2
To complete squares, we need to remember the relation:
(a + b)^2 = a^2 + 2*a*b + b^2
Now we start with:
c(x) = x^2 - 16x + 84
Let's try to transform this into the general relation:
c(x) = x^2 - 2*8*x + 84
8*8 = 64
and:
84 - 20 = 64
Thus if we add and subtract 20, we get:
c(x) = x^2 - 2*8*x + 84 + (20 - 20)
c(x) = x^2 - 2*8*x + 64 + 20
c(x) = (x - 8)^2 + 20
c(x) - 20 = (x - 8)^2
This is the quadratic equation in vertex form.
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