Solve the radical equation.

Question

sqrt5x+14=x

Answer 1

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.