Question

""Solve the radical equation √(2x+3) = x and check for extraneous solutions. Circle the solution to the equation.""

Answer 1

To solve the radical equation √(2x+3) = x, we need to isolate the radical term, rewrite the equation as a quadratic equation, factor it, and solve for x. We then check for extraneous solutions by substituting them back into the original equation.

Step-by-step explanation:

To solve the radical equation √(2x+3) = x, we need to isolate the radical term. Here are the step-by-step instructions:

1. Square both sides of the equation: (√(2x+3))^2 = (x)^2
2. Expand the left side: 2x+3 = x^2
3. Rewrite the equation as a quadratic equation: x^2 - 2x - 3 = 0
4. Factor the quadratic equation: (x - 3)(x + 1) = 0
5. Set each factor equal to zero and solve for x: x - 3 = 0 or x + 1 = 0
6. So the solutions to the equation are x = 3 and x = -1.

Now we need to check for extraneous solutions by substituting them back into the original equation. When we substitute x = 3, we get √(2(3)+3) = 3, which is true. When we substitute x = -1, we get √(2(-1)+3) = -1, which is not true. Therefore, the only solution to the equation is x = 3.