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vivado [14]
3 years ago
8

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

Mathematics
1 answer:
dmitriy555 [2]3 years ago
8 0
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}.
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