Solve.

Square root of 3x+4=x
BobPursely can you please show me the work

square both sides.

(3x+4)=x^2
rearrange
x^2-3x-4=0
solve that by factoring, or the quadratic equation.

and then test the answers in the original equation. When you square an equation, you can introduce roots that wont work.

Sure, here's how you can solve the equation √(3x+4) = x:

Step 1: Square both sides of the equation to eliminate the square root symbol:
(√(3x+4))^2 = x^2, which simplifies to 3x+4 = x^2.

Step 2: Rearrange the equation to form a quadratic equation:
x^2 - 3x - 4 = 0.

Step 3: Factorize the quadratic equation:
(x - 4)(x + 1) = 0.

Step 4: Set each factor equal to zero and solve for x:
x - 4 = 0 → x = 4,
x + 1 = 0 → x = -1.

Therefore, the equation √(3x+4) = x has two possible solutions: x = 4 and x = -1.