Solve each equation. See Examples 4–6. √x-√(x-12)=2

Key Concepts

Square Roots

Square roots are mathematical operations that find a number which, when multiplied by itself, gives the original number. In the context of the equation, understanding how to manipulate square roots is essential for isolating variables and solving for x. For example, √x represents a value that, when squared, equals x.

Isolating Variables

Isolating variables is a fundamental algebraic technique used to solve equations. This involves rearranging the equation to get the variable of interest on one side, allowing for easier computation. In the given equation, isolating the square root terms will help simplify the problem and lead to a solution for x.

Squaring Both Sides

Squaring both sides of an equation is a method used to eliminate square roots, making it easier to solve for the variable. When both sides of an equation are squared, it is crucial to remember that this can introduce extraneous solutions, so checking the final answers against the original equation is necessary to ensure validity.