SOLUTION: A Student claims that the equations sq -x =3 has no solution since the square root of a negative number does not exist. Why is this argument wrong?

Question 175234: A Student claims that the equations sq -x =3 has no solution since the square root of a negative number does not exist. Why is this argument wrong?
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
the student is wrong.
here's why.

is the original equation.
---
if you square both sides of the equation you get:
which becomes:
-x = 9 which becomes x = -9 once you multiply both sides of the equation by (-1).
---
to prove the answer is correct you substitute the value of -9 for x in the original equation.

which becomes:

which becomes:
3 = 3 proving the value of x = -9 is good.
---
i believe the student was reacting to the fact that there was a negative sign under the square root and you can't take the square root of a negative number.
---
if x is negative, however, than a minus of a minus is a plus making the solution valid.
---

RELATED QUESTIONS
can someone tell me how to answer this question? please A student claims that the... (answered by stanbon)

A student claims that the equation the !-x = 3 (square root of) has no solution, since... (answered by richwmiller)

Solve the following system of linear equations using any method. If a solution does not... (answered by ankor@dixie-net.com)

Vertical asymptote of: �(x) = (x-22)/(x^2+4) My attempt: so the vertical asymptotes... (answered by stanbon,ewatrrr)

Can you please help me find the dimensinos of a rectangle with the great area whose... (answered by scott8148)

Find the solution(s) for when f(x) = -4 if f(x) = -x^2 + 12 a. x=4 b. x=4,-4 c.... (answered by nabla)

The number of solutions for square root of (5x+7) - sq. root of (3x+1) = sq. root of... (answered by malglu)

Solve the system of linear equations. If a unique solution does not exist, state whether... (answered by amoresroy)

Evaluate limit as x goes to 2 from the left of the quotient of x and the quantity the... (answered by Boreal)