SOLUTION: what numbers multiply to -9 and add to 5

Question 1158321: what numbers multiply to -9 and add to 5

Found 2 solutions by Boreal, Theo:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
xy=-9
x+y=5
y=5-x
x(5-x)=-9
5x-x^2=-9
0=x^2-5x-9
z=(1/2)(5+/- sqrt (61)
=6.405 and -1.405

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x = one of the numbers and y = the other of the numbers.
you get:
x + y = 5
x * y = -9
solve for y in the first equation to get y = 5 - x
replace y with 5 - x in the second equation to get x * (5 - x) = -9
simplify to get 5x - x^2 = -9
subtract the left side of the equation from both sides of the equation to get:
5x - x^2 - (5x - x^2) = -9 - (5x - x^2)
simplify to get:
5x - x^2 - 5x + x^2 = 9 - 5x + x^2
combine like terms to get:
0 = 9 - 5x + x^2
reorder the terms in descending order of degree to get:
0 = x^2 - 5x - 9
switch sides to get:
x^2 - 5x - 9 = 0
solve this quadratic equation using the quadratic formula to get:
x = (-5 + sqrt(61)) / 2 or x = (-5 - sqrt(61)) / 2
use your calculator to find the decimal equivalent of these values to get:
x = 1.405124838 or x = -6.405124838
replace x with 1.405124838 in the first equation to get:
1.405124838 + y = 5
solve for y to get y = -6.405124838
replace x and y with these values in the second equation to get:
x * y = 1.405124838 * -6.405124838 = -9
the values are confirmed to be good.
your solution is that one of the numbers is 1.405124838 and the other number is -6.405124838.
the numbers shown are rounded by the calculator to 9 decimal digits.
the actual values have more decimal digits than that.

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