Solve the radical equation.
sqrt5x+14=x
To solve the radical equation, we need to isolate the radical on one side of the equation.
sqrt(5x) + 14 = x
Subtract 14 from both sides:
sqrt(5x) = x - 14
Now square both sides to eliminate the square root:
(√5x)^2 = (x - 14)^2
5x = x^2 - 28x + 196
Rearrange the equation to set it equal to zero:
x^2 - 33x + 196 = 0
Now we can factorize the quadratic equation:
(x - 28)(x - 7) = 0
Setting each factor to zero gives us two possible solutions:
x - 28 = 0 => x = 28
x - 7 = 0 => x = 7
Therefore, the solutions to the radical equation are x = 28 and x = 7.