express as an equation:one no. is six greater thanfour times the other.their product is 238?

Answer 1

x=4y+6 and xy=238.
so you get:
(4y+6)y=238
4y^2+6y=238
4y^2+6y-238=0
1/2(4y^2+6y-238)=1/2(0)
2y^2+3y-119=0
using quadratic formula, you get:
y=(-3+/-sq root[3^2-4*2*119])/(2*2)
=(-3+/-sq root[9-952])/4
=(-3+/-sq root[-943])/4

then you do 1 of 2 things:
1) if the solution set is real numbers, you stop here and say:
no solution because the square root of a negative number is not a real number
2) if the solution set is complex numbers you go on to do:
y=(-3+/-i*sq root[943])/4
because xy=238
therefore x((-3+/-i*sq root[943])/4)=238
x=238/((-3+/-i*sq root[943])/4)
=952/(-3+/-i*sq root[943])
=952/(-3+i*sq root[943]) OR 952/(-3-i*sq root[943])
=952/(-3+i*sq root[943])*(-3-i*sq root[943])/(-3-i*sq root[943]) OR 952/(-3-i*sq root[943])*(-3+i*sq root[943])/(-3+i*sq root[943])
=952(-3-i*sq root[943])/((-3+i*sq root[943])(-3-i*sq root[943])) OR 952(-3+i*sq root[943])/((-3-i*sq root[943])(-3+i*sq root[943]))
=952(-3-i*sq root[943])/((-3)^2-(i*sq root 943)^2)
OR 952(-3+i*sq root[943])/((-3)^2-(i*sq root 943)^2)
= 952(-3-i*sq root[943])/(9--943)
OR 952(-3+i*sq root[943])/(9--943)
=952(-3-i*sq root[943])/952 OR 952(-3+i*sq root[943])/952
=-3-i*sq root[943] OR -3+i*sq root[943]
making the solution sets:
y=(-3+i*sq root[943])/4 AND x=3-i*sq root[943]
OR
y=(-3-i*sq root[943])/4 AND x=3-i*sq root[943]

Note: sq root[ ] is my way of expressing the square root of a number
i is the square root of negative 1

hope that will help!

Answer 2

six greater than 4 times the other and their product is 238

4 times = 4x

six greater than 4 times other = 4x + 6

the product is 238

the equation becomes

4x + 6 = 238

solving for x

4x + 6 = 238
-6 -6

Subtracting 6 from both sides

4x = 232

4x/4 = 232/4

Dividing 4 from both sides

x = 58

4x + 6 = 238

Insert 58 into the x position

4(58) + 6 = 238

232 + 6 = 238

238 = 238

Answer 3

x be the given no: & y be the other
x=4y+6 xy=238
implies y=238/x
Putting 3rd in 1st equation
x=4(238/x)+6 gives X^2+6x-952=0

Answer 4

X = 6 + 4Y and X * Y = 238

Answer 5

let one no be a and the other b
a=4b+6 is the first equation
a*b=238 and on solving the nos will trickle out

Answer 6

make the smaller number x
the larger one is 4x + 6
so the product is x(4x + 6) = 238

Answer 7

(4y^2)+6y-238=0