SOLUTION: The square of a positive number decreased by 10 is 2 more than 4 times the number. What is the number? Trouble setting up.... any helpful sites that work with this type of ques

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Question 195935: The square of a positive number decreased by 10 is 2 more than 4 times the number. What is the number?
Trouble setting up.... any helpful sites that work with this type of question or one that can teach me? . Thanks.... frustrated mom:)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"The square of a positive number decreased by 10 is 2 more than 4 times the number" translates to x%5E2-10=4x%2B2




x%5E2-10=4x%2B2 Start with the given equation.


x%5E2-10-4x-2=0 Get all terms to the left side.


x%5E2-4x-12=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-4, and c=-12


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%281%29%28-12%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-4, and c=-12


x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%281%29%28-12%29+%29%29%2F%282%281%29%29 Negate -4 to get 4.


x+=+%284+%2B-+sqrt%28+16-4%281%29%28-12%29+%29%29%2F%282%281%29%29 Square -4 to get 16.


x+=+%284+%2B-+sqrt%28+16--48+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-12%29 to get -48


x+=+%284+%2B-+sqrt%28+16%2B48+%29%29%2F%282%281%29%29 Rewrite sqrt%2816--48%29 as sqrt%2816%2B48%29


x+=+%284+%2B-+sqrt%28+64+%29%29%2F%282%281%29%29 Add 16 to 48 to get 64


x+=+%284+%2B-+sqrt%28+64+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%284+%2B-+8%29%2F%282%29 Take the square root of 64 to get 8.


x+=+%284+%2B+8%29%2F%282%29 or x+=+%284+-+8%29%2F%282%29 Break up the expression.


x+=+%2812%29%2F%282%29 or x+=++%28-4%29%2F%282%29 Combine like terms.


x+=+6 or x+=+-2 Simplify.


Since it is specified that the number is positive, this means that the only answer is x+=+6