Question

What is the solution to the equation below? √x+2 =x-4

Answer 1

x = 9

Explanation:

Subtract 2 from both sides:

`√(x)` = x - 6

Square both sides:

x = (x - 6)^2

Expand:

x = x^2 - 12x + 36

Subtract x from both sides:

0 = x^2 - 13x + 36

Factor:

0 = (x - 4) (x - 9)

From this, we get the solutions that x is either 4 or 9. However, we need to check these solutions with the original equation.

`√(9)` + 2 = 9 - 4

3 + 2 = 9 - 4

5 = 9 - 4

5 = 5

So we know 9 works as a solution. However, when we plug in x=4:

`√(4)` + 2 = 4 - 4

2 + 2 = 4 - 4

4 = 4 - 4

4 = 0

That gives us an error. Even though we were able to solve the quadratic equation and get it as an answer, it doesn't actually work as a solution. Therefore, the only solution to this problem is x = 9.