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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Solving an Equation with Two Radical Terms

Example

Solve for x:

 SolutionStep 1 Isolate a radical term. Subtract from both sides. Step 2 Apply the Principle of Powers. = 2 Square both sides. Step 3 Solve the resulting equation. Write the right side as a product. FOIL the right side. Isolate the remaining radical term. 2x - 6 Divide both sides by 2. x - 3 Square both sides. (x - 3)2 Write the left side as a product. Simplify. Write in standard form. Factor. Use the Zero Product Property. Solve for x.Step 4 Check the solution. (x - 3)(x - 3) x2 - 6x + 9 x2 - 10x - 21 (x - 3)(x - 7) x - 3 = 0 or x - 7 x = 3 or x = 4(x - 3) = 4x - 12 = 0 = 0 = 0 = 7

Since x = 7 does not check, the only solution is x = 3.

Note:

We divide both sides by 2 rather than 4 in order to avoid introducing fractions into the equation.

One way to simplify is: