What is the answer to sqrt(3x-2)+sqrt(4-2x)=2x-2 ?

The answer to sqrt(3x-2)+sqrt(4-2x)=2x-2 is x=2

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sqrt(3x-2)+sqrt(4-2x)=2x-2

3 x - 2 + 4 - 2 x = 2 x - 2

x = 2

Solution steps

3 x - 2 + 4 - 2 x = 2 x - 2

Remove square roots

- 32 x^{3} + 128 x^{2} - 160 x + 64 = 16 x^{4} - 104 x^{3} + 249 x^{2} - 260 x + 100

Switch sides

4 x^{2} - 4 4 - 2 x x - 10 x + 4 4 - 2 x + 8 = 3 x - 2

Move

4 x^{2}

to the right side

- 4 4 - 2 x x - 10 x + 4 4 - 2 x + 8 = 3 x - 2 - 4 x^{2}

Move

10 x

to the right side

- 4 4 - 2 x x + 4 4 - 2 x + 8 = - 4 x^{2} + 13 x - 2

Move

8

to the right side

- 4 4 - 2 x x + 4 4 - 2 x = - 4 x^{2} + 13 x - 10

Factor

- 4 4 - 2 x x + 4 4 - 2 x : 4 4 - 2 x (- x + 1)

4 4 - 2 x (- x + 1) = - 4 x^{2} + 13 x - 10

Solve

- 32 x^{3} + 128 x^{2} - 160 x + 64 = 16 x^{4} - 104 x^{3} + 249 x^{2} - 260 x + 100 : x = 2, x \approx 1.10036 \dots

x = 2, x \approx 1.10036 \dots

Verify Solutions:

x = 2

True

, x \approx 1.10036 \dots

False

The solution is

x = 2

x = 2.5

4 x + 4 = x + 2

10 + 3 x = x

5 + x + 7 = x

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