Question

What is the missing constant term and a perfect square starts with x^2+10x

Answer 1

The perfect square is a number that is the product of two identical numbers. So 9 is a perfect square because it's the product of 3 * 3. For variables, perfect squares can be expressed as
`(x+a)^(2)` or
`(x-a)^(2)`, where a is some number and x is the variable.
If we expand these terms,
`(x+a)^(2)=x^(2)+2ax+a^(2)`, and
`(x-a)^(2)=x^(2)-2ax+a^(2)`. Since the given term is
`x^(2)+10x`, we can see that it's part of the perfect square
`x^(2)+2ax+a^(2)`. We just need to find
`a^(2)`.
So,
`x^(2)+2ax+a^(2)=x^(2)+10x+a^(2)`. Notice that
`10=2a`, so
`a=5`. So, the missing constant term is
`5^(2)=25`. The perfect square is
`(x+5)^(2)`.