What times what equals 270 and when added equals 7?

Answer 1

270=xy and x+y=7

x+y=7 subtract y from both sides

x=7-y now that we have x we plus into 270=xy

270=(7-y)y multiply them together

270=7y-y^2 move the 270 to the right

0=-y^2+7y-270 this problem does not factor out so we have to use the quadratic formula which is x= (-b(+ or -) (b^2 -4ac)^(1/2))/2a

A=-1 B=7 C=-270 simply plug the number into the equation

(-7(+ or -) (7^2 -4(-1)(-270)^(1/2))/2(-1)

(-7(+ or -) (49 -1080)^(1/2))/-2 then break the equation up by plus and minus

(-7(+) (-1031)^(1/2))/-2 or (-7(-) (-1031)^(1/2))/-2

(-7 + 32.109188716004645i)/-2 or (-7 - 32.109188716004645i)/-2 = y so plug in x+y=7 which equals x=7-y to find possible x values

x= (-14/-2) - (-7 + 32.109188716004645i)/-2 or x= (-14/-2) - (-7 - 32.109188716004645i)/-2

x= (-7 - 32.109188716004645i)/-2 or x= (-7 + 32.109188716004645i)/-2

So possible answers for this problem is that Y is (-7 + 32.109188716004645i)/-2 where x is (-7 - 32.109188716004645i)/-2 or that y is (-7 - 32.109188716004645i)/-2 where x is (-7 + 32.109188716004645i)/-2