Question

Solve the equation
√(5x + 10) + 8 = x. If there
is only one solution, say so. Otherwise find
the sum of the solutions.

Answer 1

\[\sqrt(5x+10) = x - 8\]
\[\sqrt(5x + 10) ^ 2 = (x - 8) ^2\]
\[5x + 10 = x^2 - 16x + 64\]
\[0 = x^2 - 21x + 54\]
\[0 = (x-18)(x-3)\]
Therefore x = 18 and x = 3 are possible solution.
Check each solution.
checking x = 18
\[\sqrt(5*18 + 10) = 18 - 8\]
\[\sqrt(100) = 10\]
\[10 = 10\]
x = 18 is a solution

checking x = 3
\[\sqrt(5*3+10) = 3 - 8\]
square roots can't be negative. Therefore x = 3 is not a souliton

Answer 2

Thanks so much, you're a lifesaver!