What is the answer to 2x-4/(sqrt(2x-4))-4=0 ?

The answer to 2x-4/(sqrt(2x-4))-4=0 is x\approx 3.25992…

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2x-4/(sqrt(2x-4))-4=0

Solution

2 x - \frac{4}{2 x - 4} - 4 = 0

Solution

x \approx 3.25992 \dots

Solution steps

2 x - \frac{4}{2 x - 4} - 4 = 0

Multiply both sides by

2 x - 4

2 x 2 x - 4 - \frac{4}{2 x - 4} 2 x - 4 - 4 2 x - 4 = 0 \cdot 2 x - 4

Simplify

2 2 x - 4 x - 4 - 4 2 x - 4 = 0

Move

4

to the right side

2 2 x - 4 x - 4 2 x - 4 = 4

Move

4

to the left side

2 2 x - 4 x - 4 2 x - 4 - 4 = 0

Factor

2 2 x - 4 x - 4 2 x - 4 - 4 : 2 (x 2 x - 4 - 2 2 x - 4 - 2)

2 (x 2 x - 4 - 2 2 x - 4 - 2) = 0

Divide both sides by

2

x 2 x - 4 - 2 2 x - 4 - 2 = 0

Move

2

to the right side

x 2 x - 4 - 2 2 x - 4 = 2

Factor

x 2 x - 4 - 2 2 x - 4 : 2 x - 4 (x - 2)

2 x - 4 (x - 2) = 2

Divide both sides by

x - 2

2 x - 4 = \frac{2}{x - 2}

Square both sides:

2 x - 4 = \frac{4}{x ^{2} - 4 x + 4}

2 x - 4 = \frac{4}{x ^{2} - 4 x + 4}

Solve

2 x - 4 = \frac{4}{x ^{2} - 4 x + 4} : x \approx 3.25992 \dots

x \approx 3.25992 \dots

Verify Solutions:

x \approx 3.25992 \dots

True

The solution is

x \approx 3.25992 \dots

Popular Examples

x-3sqrt(x)=-2

x - 3 x = - 2

sqrt(x-2)+sqrt(x-13)=11

x - 2 + x - 13 = 11

sqrt(x-3)=1

x - 3 = 1

x-4=sqrt(x)

x - 4 = x

405=5(9x)^{4/3}

405 = 5 (9 x)^{\frac{4}{3}}

Frequently Asked Questions (FAQ)

What is the answer to 2x-4/(sqrt(2x-4))-4=0 ?
The answer to 2x-4/(sqrt(2x-4))-4=0 is x\approx 3.25992…
Solve for x: 2x-4/(sqrt(2x-4))-4=0
The solution is x\approx 3.25992…

2x-4/(sqrt(2x-4))-4=0

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to 2x-4/(sqrt(2x-4))-4=0 ?

Solve for x: 2x-4/(sqrt(2x-4))-4=0