What is the answer to 9(sqrt(4x+1)-sqrt(3x-2))=x+3 ?

The answer to 9(sqrt(4x+1)-sqrt(3x-2))=x+3 is x=6

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9(sqrt(4x+1)-sqrt(3x-2))=x+3

Solution

9 (4 x + 1 - 3 x - 2) = x + 3

Solution

x = 6

Solution steps

9 (4 x + 1 - 3 x - 2) = x + 3

Expand

9 (4 x + 1 - 3 x - 2) : 9 4 x + 1 - 9 3 x - 2

9 4 x + 1 - 9 3 x - 2 = x + 3

Remove square roots

972 x^{3} + 5184 x^{2} + 4860 x - 5832 = x^{4} - 150 x^{3} + 5157 x^{2} + 35100 x + 54756

Switch sides

x^{2} + 18 x 3 x - 2 + 249 x + 54 3 x - 2 - 153 = 324 x + 81

Move

x^{2}

to the right side

18 x 3 x - 2 + 249 x + 54 3 x - 2 - 153 = 324 x + 81 - x^{2}

Move

249 x

to the right side

18 x 3 x - 2 + 54 3 x - 2 - 153 = - x^{2} + 75 x + 81

Move

153

to the right side

18 x 3 x - 2 + 54 3 x - 2 = - x^{2} + 75 x + 234

Factor

18 x 3 x - 2 + 54 3 x - 2 : 18 3 x - 2 (x + 3)

18 3 x - 2 (x + 3) = - x^{2} + 75 x + 234

Solve

972 x^{3} + 5184 x^{2} + 4860 x - 5832 = x^{4} - 150 x^{3} + 5157 x^{2} + 35100 x + 54756 : x = - 3, x = 6, x = 1122

x = - 3, x = 6, x = 1122

Verify Solutions:

x = - 3

False

, x = 6

True

, x = 1122

False

The solution is

x = 6

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Frequently Asked Questions (FAQ)

What is the answer to 9(sqrt(4x+1)-sqrt(3x-2))=x+3 ?
The answer to 9(sqrt(4x+1)-sqrt(3x-2))=x+3 is x=6
Solve for x: 9(sqrt(4x+1)-sqrt(3x-2))=x+3
The solution is x=6

9(sqrt(4x+1)-sqrt(3x-2))=x+3

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to 9(sqrt(4x+1)-sqrt(3x-2))=x+3 ?

Solve for x: 9(sqrt(4x+1)-sqrt(3x-2))=x+3