Question

solve √x+1 +5=x (the "+5" isnt under the radical)

Answer 1

\[\sqrt{x+1}=x-5\]

Answer 2

√x+1 = x - 5
square both sides
x + 1 = (x - 5)^2

Answer 3

\[x+1=x^2-10x+25\]

Answer 4

\[x^2-11x+24=0\]

Answer 5

this rearranges to x^2 -11x + 24 = 0

Answer 6

\[(x-3)(x-8)=0\]

Answer 7

\[x=3, x=8\]

Answer 8

Must always check the answers after squaring.

Answer 9

so what your saying is +3, and +8 are both x?? @Mertsj

Answer 10

x + 1 = x^2 - 10x + 25
x^2 - 11x + 24 = 0
(x - 8)(x - 3) = 0
x = 8, 3
Check for extraneous solutions by plugging it back in.
√(x + 1) + 5 = x
√(9) + 5 = 8
3 = 3
√(x + 1) + 5 = x
√(4) + 5 = 3
2 + 5 ≠ 3
THe solution is x = 8