1. The square of an interger is 30 more than the integer. Find the integer.
I tried.... x^2 = x+30 to get a solution of x=6 and x-5
I am unsure if this is the right equation for the problem above.
Then by all means learn to check your solutions. Remember, when you
check a WORD problem, you check each solution in the WORDS, never in
the equation, for you might have the right answer to the wrong
equation!
Here, let's go a-checking. It's easy.
The first sentence says:
>>...The square of an integer is 30 more than the integer...<<
Check that with 6. In other words, is it true that:
the square of 6 is 30 more than 6?
the square of 6 is 36, and lo and behold, 36 really is 30
more than 6. !!!
So we know that 6 is correct.
But we still have another solution to check, x=-5
Again, the first sentence says:
>>...The square of an integer is 30 more than the integer...<<
Check that now with -5. In other words, is it true that:
the square of -5 is 30 more than 6.
the square of -5, or (-5)² is +25 and, holy smokes, +25
really is 30 more than -5. !!!
So we know that -5 is also correct.
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2. The sum of an integer and its square is 30. Find the number.
I tried..... x + x^2= 30 to get a solution of x=-6 and x=5
Then you should check these two solutions.
The first sentence says:
>>...The sum of an integer and its square is 30...<<
Check that with -6. In other words, is it true that:
the sum of -6 and its square is 30?
The square of -6 is +36 and heyyy, the sum of -6 and 36
really is 30. !!!
So we know that -6 is correct.
But we still have another solution to check, x=5
So we check that with 5. In other words, is it true that:
the sum of 5 and its square is 30?
The square of 5 is 25 and whaddayaknow, the sum
of 5 and 25 really is 30. !!!
So we know that 5 is correct.
See how easy it is to check a number back into the
words to see if it is the correct answer?
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Edwin