Problem 1) √4 - x = -2

x -2 x -2

Problem 2) √x + 2 - x = 0

Was confused on the answers; please re-advise

Problem 1) √4 - x = -2

x -2 x -2

Problem 2) √x + 2 - x = 0

Was confused on the answers; please re-advise

Tutors, sign in to answer this question.

sqrt(4) = 2.

For 2 - x/(x-2) = -2/(x-2) start by multiplying through by (x-2) to get the variable out of the denominator. This gives:

2*(x-2) - x = -2. Expand this out, then combine the constant terms on one side and variable terms on the other.

2*x - 2*2 - x = -2

2*x - x = 4 - 2 Factor out the coefficients in front of x

(2-1)*x = 2 Divide to isolate x

x = 2

If you set x = 2 in the original equation, the result is to divide by 0 so it is not a valid solution.

For sqrt(x) + 2 - x = 0, I like to do this with a substitution by defining another variable y = sqrt(x).

The new equation becomes

y + 2 - y^{2} = 0, multiply by -1

y^{2} -y - 2 = 0

(y-2)(y+1) = 0

y = 2, -1

Since y = sqrt(x), x = y^2, so:

x = 4, 1

However, plugging these back into the original equation shows that only x =4 is a valid solution. This is because the sqrt(x) cannot equal (-1).

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Michael D.

Do you need help in Science? Math? Regents or SAT? Ask a Geologist!

$13.75 per 15 min

View Profile >

Richard W.

Replace anxiety with confidence. Math can be fun!

$11.25 per 15 min

View Profile >

Alexis G.

All-Subject/Test Prep Tutor, Specializing in Language Instruction

$11.25 per 15 min

View Profile >