One number is 58 more than twice another. Their product is 58 more than twice their sum. Find the numbers.
one number --- x
the other ------2x+58
their product = x(2x+58)
their sum = 3x + 58
x(2x+58)= 2(3x+58) + 58
2x^2 + 58x = 6x + 116 + 58
2x^2 + 52x - 174 = 0
(x-3)(2x + 58) = 0
x = 3 or x = -58/2 = -29
if x = 3
one number is 3, the other is 64
if x = -29
one number is = -29, the other is 0
check:
if x = 3, one is 3 the other is 64
product = 192
sum = 67 --> twice the sum = 134
difference between 192 and 134 is 58 , so correct
if x = -29, one is -29, the other is 0
product = 0
sum = -29 --> twice the sum = -59
difference between 0 and -58 is 58
all is good!