Question

Solve the following equation for x: x(abs(x-9))= 40x +9. Find the four roots.
Solve: 4(abs(b))-1=11.

Answer 1

\[4|b|-1=11\\
4|b|=12\\
|b|=3\\
b=3,b=-3\] should do it

Answer 2

do you know how to solve the first one? @satellite73

Answer 3

thanks doe

Answer 4

*though

Answer 5

i think we can do that too
it is a bit harder

Answer 6

\[x|x-9|=40x+9\] right?

Answer 7

yes

Answer 8

we have to work in cases
if \(x>9\) then \(|x-9|=x-9\) and the equation becomes
\[x(x-9)=40x+9\]

Answer 9

for that case you get the quadratic equation
\[x^2-49x-9=0\] if my algebra is correct
quadratic formula will give the two answers

Answer 10

if \(x<9\) then \(|x-9|=-x+9\) and you get another quadratic equation starting with
\[x(-x+9)=40x+9\] more algebra gives \[x^2+31x+9=0\]and the quadratic formula will give two more answers
odd that this problem is way more complicated than the second one which is rather easy
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Answer 11

thanks!

Answer 12

yw