SOLUTION: What number multiplied equals -6 and adds 7

Question 1135310: What number multiplied equals -6 and adds 7

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let a be one of the numbers and let b be the other of the numbers.

you get a * b = -6 and you get a + b = 7

in the second equation, solve for a to get a = 7 - b.

in the first equation, replace a with 7 - b to get (7 - b) * b = -6.

simplify this to get 7b - b^2 = -6

subtract 7b and add b^2 to both sides of the equation to get 0 = b^2 - 7b - 6

this is the same as b^2 - 7b - 6 = 0

factor this equation using the quadratic formula to get:

b = 7.772001873 or b = -.7720018727.

solve for a in the first equation to get:

when b = 7.772001873, a= -6 / 7.772001873 = -.7720018727.

when b = -.7728018727, a = -6 / -.7720018727 = 7.7720018727.

add them together, you get 7.

multiply them together you get -6.

so you have two possible answers.

a = -.7720018727 when b = 7.772001873

a = 7.772001873 when b = -.7720028727

your answer should be that one of the numbers is equal to 7.772001873 and the other number is -.7720028727

multiply them together, you get -6.

add them together, you get 7.

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