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

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

Solve for x: 2x^2sqrt(x-2)=sqrt(x-2)

The solution is x=2,x=-1/(sqrt(2)),x= 1/(sqrt(2))

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

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

Decimal Notation

x = 2, x = - 0.70710 \dots, x = 0.70710 \dots

Solution steps

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

Move

x - 2

to the left side

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 2 = 0 : x = 2

Solve

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

Solve

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

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

Verify Solutions:

x = 2

True

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

True

, x = \frac{1}{2}

True

The solutions are

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

5 2 x - 4 = 6

D = 53 Q^{0.18}

\frac{2 x}{5} = 4

x - 3 = 13

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