The difference of the square of a number and 18 is equal to 7 times that number. Find the negative solution.

Question

reduce it to the simplest form

Answer 1

|x^2-18| = 7x

x^2 -18 = 7x

x^2 -7x -18 = 0

(x-9)(x+2) = 0

x =9 or -2

-2 is a negative solution

(-2)^2 -18 = 4-18=-14

-2(7) = -14

or

18-x^2 = 7x

x^2 +7x -18 = 0

(x+9)(x-2) = 0

x=-9 or 2

-9 is another possible negative solution

18-(-9)^2 = 18-81= -63

7(-9) = -63

but you probably want -2

as "difference" of two numbers usually means the 1st number minus the second number

although it's also often used to mean the absolute value of the difference of the two numbers, such as the difference in height of two people usually means a positive number regardless which person is taller