A radical equation is one in which one of the variables is under a radical.

To resolve a radical equation, do the following:

- Step 1: Isolate the radical expression involving the variable. If more than one radical expression involves the variable, then isolate one of them.
- Step 2: Raise both sides of the equation to the index of the radical.
- Step 3: If there is still a radical equation, repeat steps 1 and 2; otherwise, solve the resulting equation.
- Step 4: Check the answer in the original equation.

Solve $\sqrt{3x^2 + 10x} - 5 = 0$.

Step1:

Isolate the radical part

$\sqrt{3x^2 + 10x} = 5$

Step2:

Raise both sides to the index of the radical and square both sides.

Step3:

Apply the quadratic formula:

Step4:

Check the result:

Then, we need to check the result for x = -5, so here’s what we get:

Answer: $x = -5 or x = \frac{5}{3}$.

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