What is the answer to ((x-4))/((sqrt(x)+2))=x-8 ?

The answer to ((x-4))/((sqrt(x)+2))=x-8 is x=9

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((x-4))/((sqrt(x)+2))=x-8

Solution

\frac{( x - 4 )}{( x + 2 )} = x - 8

Solution

x = 9

Solution steps

\frac{( x - 4 )}{( x + 2 )} = x - 8

Multiply both sides by

x + 2

\frac{x - 4}{x + 2} (x + 2) = x (x + 2) - 8 (x + 2)

Simplify

x - 4 = x (x + 2) - 8 (x + 2)

Expand

x (x + 2) - 8 (x + 2) : x x + 2 x - 8 x - 16

x - 4 = x x + 2 x - 8 x - 16

Factor

x x + 2 x - 8 x - 16 : (x + 2) (x - 8)

x - 4 = (x + 2) (x - 8)

Square both sides:

x^{2} - 8 x + 16 = x^{3} + 4 x x^{2} - 12 x^{2} - 64 x x + 256 x + 256

x^{2} - 8 x + 16 = x^{3} + 4 x x^{2} - 12 x^{2} - 64 x x + 256 x + 256

Switch sides

x^{3} + 4 x x^{2} - 12 x^{2} - 64 x x + 256 x + 256 = x^{2} - 8 x + 16

Move

x^{3}

to the right side

4 x x^{2} - 12 x^{2} - 64 x x + 256 x + 256 = x^{2} - 8 x + 16 - x^{3}

Move

12 x^{2}

to the right side

4 x x^{2} - 64 x x + 256 x + 256 = - x^{3} + 13 x^{2} - 8 x + 16

Move

256

to the right side

4 x x^{2} - 64 x x + 256 x = - x^{3} + 13 x^{2} - 8 x - 240

Factor

4 x x^{2} - 64 x x + 256 x : 4 x (x^{2} - 16 x + 64)

4 x (x^{2} - 16 x + 64) = - x^{3} + 13 x^{2} - 8 x - 240

Square both sides:

16 x^{5} - 512 x^{4} + 6144 x^{3} - 32768 x^{2} + 65536 x = x^{6} - 26 x^{5} + 185 x^{4} + 272 x^{3} - 6176 x^{2} + 3840 x + 57600

16 x^{5} - 512 x^{4} + 6144 x^{3} - 32768 x^{2} + 65536 x = x^{6} - 26 x^{5} + 185 x^{4} + 272 x^{3} - 6176 x^{2} + 3840 x + 57600

Solve

16 x^{5} - 512 x^{4} + 6144 x^{3} - 32768 x^{2} + 65536 x = x^{6} - 26 x^{5} + 185 x^{4} + 272 x^{3} - 6176 x^{2} + 3840 x + 57600 : x = 4, x = 9, x = \frac{21 + 41}{2}, x = \frac{21 - 41}{2}

x = 4, x = 9, x = \frac{21 + 41}{2}, x = \frac{21 - 41}{2}

Verify Solutions:

x = 4

False

, x = 9

True

, x = \frac{21 + 41}{2}

False

, x = \frac{21 - 41}{2}

False

The solution is

x = 9

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sqrt(5x^2-6x+8)-sqrt(5x^2-6x-7)=1

5 x^{2} - 6 x + 8 - 5 x^{2} - 6 x - 7 = 1

sqrt(4x^2-15)-2x=-1

4 x^{2} - 15 - 2 x = - 1

x=1+sqrt(3x+15)

x = 1 + 3 x + 15

(sqrt(x-2)+1)/3 =5

\frac{x - 2 + 1}{3} = 5

sqrt(22-x*\sqrt{10)}=sqrt(20)+sqrt(2)

22 - x \cdot 10 = 20 + 2

Frequently Asked Questions (FAQ)

What is the answer to ((x-4))/((sqrt(x)+2))=x-8 ?
The answer to ((x-4))/((sqrt(x)+2))=x-8 is x=9
Solve for x: ((x-4))/((sqrt(x)+2))=x-8
The solution is x=9

((x-4))/((sqrt(x)+2))=x-8

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to ((x-4))/((sqrt(x)+2))=x-8 ?

Solve for x: ((x-4))/((sqrt(x)+2))=x-8