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If 6 is added to the square of an integer, the result is 3 less than 10 times that integer. Find the integer(s).

User Musketyr
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1 Answer

6 votes

Answer:

x=9 and x=1

Explanation:

If 6 is added to the square of an integer, the result is 3 less than 10 times that integer.

x^2 +6 = 10x-3

Subtract 10x from each side.

x^2 -10x +6 = 10x-10x-3

x^2 -10x +6 = -3

Now add 3 to each side.

x^2 -10x +6+3 = -3+3

x^2 -10x +9 = 0

Now we can factor the left side of the equation.

What numbers multiply together to give positive 9 and add together to give -10?

-9* -1 = 9 -9+-1 = -10


(x-9) * (x-1) = 0

Using the zero product property

x-9 = 0 and x-1 = 0

x-9+9 = 0+9 x-1+1 = 0+1

x=9 and x=1