Algebra II Help √x+5 = x-1

√x+5 = x-1
Square root of x+5 = x-1

So, the possible answers are...
a. x = 4
b. No Solution
c. x = -1 or x = 4
d. x = -1

This was a question I missed on a test. I said the answer was "c." and my teacher marked it wrong. Can you explain why?

Erm, ill assume you mean √(x+5) on the left hand side

Square both sides to get:

x+5 = (x - 1)*(x - 1)

Multiply out the brackets:

x + 5 = x^2 - 2x + 1

x^2 - 3x - 4 = 0

(x - 4)(x + 1) = 0

So x = 4 or x = -1

I think your teacher made a mistake... =]

If you take the answers that you chose and plug them back in for "x" in the original problem, you will discover why it is wrong. The square root of -1+5=2, while -1-1= -2...so they are not equal making -1 an incorrect solution...so even though when you solved for "x" you came up with 4 and -1, you should make a habit of plugging the answers in for "x" just to make sure they work. ;)

√x+5-5 = x-1-5

√x = x - 6

x = x^2 - 12x + 36 by squaring both sides

x-x = x^2 - 12x + 36 -x

x^2 - 13x + 36 = 0

using quadratic formula you get:

[13 +/- √(169 - 144)]/2 = (13 +/- 5)/2

S = {4, 9}

You should know that -1 cannot be a solution because you cannot take the square root of -1.