Question

help please?
In solving the equation (x + 4)(x – 7) = -18, Eric stated that the solution would be
x + 4 = -18 => x = -22
or
(x – 7) = -18 => x = -11
However, at least one of these solutions fails to work when substituted back into the original equation. Why is that? Please help Eric to understand better; solve the problem yourself, and explain your reasoning.

Answer 1

the reason eric's solution doesn't work is cebause he is not solving at y= 0, he is solving at y=-18. in order to find the roots of an equation, you must solve it at y=0

so in this case we must first multiply out our equation:

(x+4)(x-7)=x^2 -3x-28 = -18

to get y= 0 our equation changes

x^2-3x-28 = -18
x^2-3x -10=0 (by adding 18 to both sides)
when we factor this equation we get:

x^2-3x -10= (x-5)(x-2)=0

so the solutions to the equation are actually:

x-5=0
x=5
x+2=0
x=-2

when we check these in our original equation they should work

Answer 2

thank you thank you thank you! that one stumped me so much!

Answer 3

np