SOLUTION: Twice the square of a certain postive number is 144 more than twice the number. What is the number? Really looking for help on how to set up.... can solve but can't seem to fig

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Question 195933: Twice the square of a certain postive number is 144 more than twice the number. What is the number?
Really looking for help on how to set up.... can solve but can't seem to figure out how to set the thing up. Thanks.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You're probably hung up on the translation:

"Twice the square of a certain postive number" ----> 2x%5E2
"is" ---> =
"144 more than twice the number" ----> 2x%2B144


So the full translation is 2x%5E2=2x%2B144



2x%5E2=2x%2B144 Start with the given equation.


2x%5E2-2x-144=0 Get all terms to the left side.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=2, b=-2, and c=-144


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-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%282%29%28-144%29+%29%29%2F%282%282%29%29 Plug in a=2, b=-2, and c=-144


x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%282%29%28-144%29+%29%29%2F%282%282%29%29 Negate -2 to get 2.


x+=+%282+%2B-+sqrt%28+4-4%282%29%28-144%29+%29%29%2F%282%282%29%29 Square -2 to get 4.


x+=+%282+%2B-+sqrt%28+4--1152+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-144%29 to get -1152


x+=+%282+%2B-+sqrt%28+4%2B1152+%29%29%2F%282%282%29%29 Rewrite sqrt%284--1152%29 as sqrt%284%2B1152%29


x+=+%282+%2B-+sqrt%28+1156+%29%29%2F%282%282%29%29 Add 4 to 1152 to get 1156


x+=+%282+%2B-+sqrt%28+1156+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%282+%2B-+34%29%2F%284%29 Take the square root of 1156 to get 34.


x+=+%282+%2B+34%29%2F%284%29 or x+=+%282+-+34%29%2F%284%29 Break up the expression.


x+=+%2836%29%2F%284%29 or x+=++%28-32%29%2F%284%29 Combine like terms.


x+=+9 or x+=+-8 Simplify.

Remember, the problem stated that the number is positive. So the only answer is x+=+9