What is the answer to 3x+sqrt(2x-2)=2sqrt(2x-2)+23 ?

The answer to 3x+sqrt(2x-2)=2sqrt(2x-2)+23 is x=9

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3x+sqrt(2x-2)=2sqrt(2x-2)+23

3 x + 2 x - 2 = 2 2 x - 2 + 23

x = 9

Solution steps

3 x + 2 x - 2 = 2 2 x - 2 + 23

Move

3 x

to the right side

2 x - 2 = 2 2 x - 2 + 23 - 3 x

Move

2 2 x - 2

to the left side

- 2 x - 2 = 23 - 3 x

Square both sides:

2 x - 2 = 529 - 138 x + 9 x^{2}

2 x - 2 = 529 - 138 x + 9 x^{2}

Solve

2 x - 2 = 529 - 138 x + 9 x^{2} : x = 9, x = \frac{59}{9}

x = 9, x = \frac{59}{9}

Verify Solutions:

x = 9

True

, x = \frac{59}{9}

False

The solution is

x = 9

17 - 2 3 x + 10 = 1

3 x - 14 = - 5

5 x^{2} + 3 x = 4 x x^{2} + 3 x + 16

x + 4 - 3 = 2

x + 85 + 11 = 20

What is the answer to 3x+sqrt(2x-2)=2sqrt(2x-2)+23 ?
The answer to 3x+sqrt(2x-2)=2sqrt(2x-2)+23 is x=9
Solve for x: 3x+sqrt(2x-2)=2sqrt(2x-2)+23
The solution is x=9