SOLUTION: If three times the square of a negative number is added to the product of -7 and the number the result is 20. Find the number.

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Question 307202: If three times the square of a negative number is added to the product of -7 and the number the result is 20. Find the number.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The phrase "three times the square of a negative number is added to the product of -7 and the number the result is 20." translates to 3x%5E2-7x=20 where 'x' is a negative number.


3x%5E2-7x=20 Start with the given equation.


3x%5E2-7x-20=0 Subtract 20 from both sides.


Notice that the quadratic 3x%5E2-7x-20 is in the form of Ax%5E2%2BBx%2BC where A=3, B=-7, and C=-20


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-%28-7%29+%2B-+sqrt%28+%28-7%29%5E2-4%283%29%28-20%29+%29%29%2F%282%283%29%29 Plug in A=3, B=-7, and C=-20


x+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%283%29%28-20%29+%29%29%2F%282%283%29%29 Negate -7 to get 7.


x+=+%287+%2B-+sqrt%28+49-4%283%29%28-20%29+%29%29%2F%282%283%29%29 Square -7 to get 49.


x+=+%287+%2B-+sqrt%28+49--240+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-20%29 to get -240


x+=+%287+%2B-+sqrt%28+49%2B240+%29%29%2F%282%283%29%29 Rewrite sqrt%2849--240%29 as sqrt%2849%2B240%29


x+=+%287+%2B-+sqrt%28+289+%29%29%2F%282%283%29%29 Add 49 to 240 to get 289


x+=+%287+%2B-+sqrt%28+289+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%287+%2B-+17%29%2F%286%29 Take the square root of 289 to get 17.


x+=+%287+%2B+17%29%2F%286%29 or x+=+%287+-+17%29%2F%286%29 Break up the expression.


x+=+%2824%29%2F%286%29 or x+=++%28-10%29%2F%286%29 Combine like terms.


x+=+4 or x+=+-5%2F3 Simplify.


So the possible solutions are x+=+4 or x+=+-5%2F3


Keep in mind that 'x' is a negative number. So the only answer is x+=+-5%2F3