SOLUTION: Remove the radicals and simplify the following equation (x-3)^1/2 + (2x)^1/2 = 3

Question 150900: Remove the radicals and simplify the following equation
(x-3)^1/2 + (2x)^1/2 = 3
Found 2 solutions by jim_thompson5910, mangopeeler07:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Convert the equation from rational exponent notation to radical notation.

Subtract from both sides.

Square both sides.

FOIL

Subtract 9 from both sides. Subtract from both sides.

Combine like terms.

Square both sides.

Multiply

FOIL.

Subtract from both sides.

Combine like terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

Break up the fraction.

Reduce.

or Break up the expression.

So the possible answers are or

However, if you plug in , the equation will not be true.

So the only answer is
Answer by mangopeeler07(462) (Show Source): You can put this solution on YOUR website!

Take the square root of x-3 and 2x and add them

Square both sides

Combine like terms on the left side

Add 3 to both sides

Divide both sides by 3

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