What is the answer to 2x^2sqrt(x-2)=xsqrt(x-2) ?

The answer to 2x^2sqrt(x-2)=xsqrt(x-2) is x=2,x= 1/2

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2x^2sqrt(x-2)=xsqrt(x-2)

2 x^{2} x - 2 = x x - 2

x = 2, x = \frac{1}{2}

Decimal Notation

x = 2, x = 0.5

Solution steps

2 x^{2} x - 2 = x x - 2

Move

x x - 2

to the left side

2 x^{2} x - 2 - x x - 2 = 0

Factor

2 x^{2} x - 2 - x x - 2 : x - 2 x (2 x - 1)

x - 2 x (2 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or x = 0 or 2 x - 1 = 0

Solve

x - 2 = 0 : x = 2

Solve

2 x - 1 = 0 : x = \frac{1}{2}

x = 2, x = 0, x = \frac{1}{2}

Verify Solutions:

x = 2

True

, x = 0

False

, x = \frac{1}{2}

True

The solutions are

x = 2, x = \frac{1}{2}

5 + 4 x = x

(4 x - 1)^{\frac{3}{2}} - 2 = 18

3 2 x - 1 = 3 x

2 x - 14 = x + 1

x + 2 - x - 1 = 1

What is the answer to 2x^2sqrt(x-2)=xsqrt(x-2) ?
The answer to 2x^2sqrt(x-2)=xsqrt(x-2) is x=2,x= 1/2
Solve for x: 2x^2sqrt(x-2)=xsqrt(x-2)
The solution is x=2,x= 1/2