Question

Does the following equation have a solution? Explain why or why not, and support your answer with a graph:
abs(-x^2-3x+5)=-4

Answer 1

it is unlikely that the absolute value of anything is negative, since the absolute value of anything is always greater than or equal to zero

Answer 2

When the absolute value is presented like this in the equation it can be a negative - if you wanted to get rid of the absolute value portion for solving reasons, you would just take the positive of everything inside the absolute value brackets and continue.

Answer 3

is this the question
\[|-x^2-3x+5|=-4\]??

Answer 4

Yep!

Answer 5

then there is no solution because the expression on the left is never negative, but \(-4\) is negative

Answer 6

But wouldn't we be able to solve it for x? Cause I can get to \[x^2+3x=1\] but I just don't know what to do from there.

Answer 7

I want to reassure you that it can be solved for x. http://www.wolframalpha.com/input/?i=%28-x%5E2-3x%2B5%29%3D-4

Answer 8

Sweet, thanks!

Answer 9

Wait.
It's true that \[x^2 + 3x = 1\] has a solution

Answer 10

However, your first equation does not

Answer 11

Absolute value implies that both
(-x^2-3x+5)=-4
and (-x^2-3x+5)=4
have a solution

Answer 12

(-x^2-3x+5)=4
has a solution, but it's complex

Answer 13

That complex solution would have square roots and fractions, right?

Answer 14

It's square root of a negative number.
The solution is (-3 +- (rad)-4)2

Answer 15

http://www.wolframalpha.com/input/?i=%28-x%5E2-3x%2B5%29%3D-4 because this says it can be solved, I just can't get there