Solving Radical Equations

Solving Radical Equations

How to solve radical equations: example and its solution.

Example

Find the value of x. Square root (x + 6) = x.

First, find the range of x.

x + 6 is the radicand of the square root.
So x + 6 ≥ 0.
x ≥ -6

x + 6 ≥ 0.
So √x + 6 = x ≥ 0
x ≥ 0

The intersection of both inequalities is x ≥ 0.

To remove the radical sign,
square both sides.

Solve the quadratic equation by factoring.

Then x = -2, 3.

See if x = -2, 3 is in x ≥ 0.

x = -2 is not in x ≥ 0.

So x = 3 is the answer.