Question

What multiplies to -29 and adds to 1

Answer 1

first set up equation
x times y=xy

so
xy=-29
and
x+y=1
subtract x from both sides
y=1-x
subsitute 1-x for y in first equation
x(1-x)=-29
distribute
x-x^2=-29
add x^2 to both sides
x=-29+x^2
subtract x from both sides
0=x^2-x-29
so we can use the quadratic formula to solve for x if the equation=0 and it is in ax^2+bx+c form so

if
ax+bx+c=0 then x=
`( -b+/-√(b^2-4ac) )/(2a)` that means x=
`( -b-√(b^2-4ac) )/(2a)` or x=
`( -b-√(b^2-4ac) )/(2a)` so


x^2-x-29
a=1
b=-1
c=-29

`( -(-1)-√(-1^2-4(1)(-29)) )/(2(1))`=
`( +1-√(1^2-(-116)) )/(2(1))=( +1-√(1^2+116) )/(2)=( +1-√(117) )/(2)= (1-10.816653826392)/(2) = [tex] (-9.816653826392)/(2)= -4.908326913196`



the second number is

`image`


the two numbers are
5.908326913196 and
-4.908326913196