« Solving Quadratic Equation

A "radical" equation is an equation in which there is a variable inside the radical sign

Four steps to solve equations with radicals

Step 1: Isolate the radicals to left side of the equal sign.

Step 2: Square each side of the equation

Step 3: Solve the resulting equation

Step 4: Check all solutions

Equations with one radical

Example 1: Solve

Solution

Step 1: Isolate the radicals to left side of the equal sign.

Step 2: Square each side of the equation

Step 3: Solve the resulting equation

Step 4: Check all solutions

Let's check to see if x₁ = 3 is solution:

Let's check to see if x₂ = -1 is solution:

So, the original equation had a single solution x = 3 .

Exercise 1: Solve equations

Example 2: Solve

Solution

Let’s check it to see if x = 1 is a solution to the original equation.

So, the original equation had no solutions.

Exercise 2: Solve equations

Equations with two radicals

Example 3: Solve

Solution

First thing to do is get one of the square roots by itself.

We have managed to eliminate one of square roots!! We will continue to work this problem as we did in the previous examples.

Let’s check both possible solutions. We will start with x = 0.

Now let’s check x = 4.

Exercise 3: Solve equations