What is the answer to 3-sqrt(x)=sqrt(2\sqrt{x)-3} ?

The answer to 3-sqrt(x)=sqrt(2\sqrt{x)-3} is x=4

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3-sqrt(x)=sqrt(2\sqrt{x)-3}

3 - x = 2 x - 3

x = 4

Solution steps

3 - x = 2 x - 3

Square both sides:

9 - 6 x + x = 2 x - 3

9 - 6 x + x = 2 x - 3

Move

x

to the right side

9 - 6 x = 2 x - 3 - x

Move

9

to the right side

- 6 x = 2 x - x - 12

Move

2 x

to the left side

- 8 x = - x - 12

Divide both sides by

- 8

x = - \frac{- x - 12}{8}

Square both sides:

x = \frac{x ^{2}}{64} + \frac{3 x}{8} + \frac{9}{4}

x = \frac{x ^{2}}{64} + \frac{3 x}{8} + \frac{9}{4}

Solve

x = \frac{x ^{2}}{64} + \frac{3 x}{8} + \frac{9}{4} : x = 36, x = 4

x = 36, x = 4

Verify Solutions:

x = 36

False

, x = 4

True

The solution is

x = 4

3 x + 7 = 0

3 x - 5 + 3 x + 3 + 1 = 0

(0.3 x)^{2} + x^{2} = 30

x^{9} = x^{3}

3 = 49 - x^{2}

What is the answer to 3-sqrt(x)=sqrt(2\sqrt{x)-3} ?
The answer to 3-sqrt(x)=sqrt(2\sqrt{x)-3} is x=4
Solve for x: 3-sqrt(x)=sqrt(2\sqrt{x)-3}
The solution is x=4