What is the answer to sqrt(4x-3)=2+sqrt(2x+5) ?

The answer to sqrt(4x-3)=2+sqrt(2x+5) is x=2(5+sqrt(21))

Solve for x: sqrt(4x-3)=2+sqrt(2x+5)

The solution is x=2(5+sqrt(21))

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4 x - 3 = 2 + 2 x + 5

x = 2 (5 + 21)

Decimal Notation

x = 19.16515 \dots

Solution steps

4 x - 3 = 2 + 2 x + 5

Remove square roots

4 x^{2} - 48 x + 144 = 32 x + 80

Solve

4 x^{2} - 48 x + 144 = 32 x + 80 : x = 2 (5 + 21), x = 2 (5 - 21)

x = 2 (5 + 21), x = 2 (5 - 21)

Verify Solutions:

x = 2 (5 + 21)

True

, x = 2 (5 - 21)

False

The solution is

x = 2 (5 + 21)

(x + 3) - 4 x + 3 - 5 = 0

75 x + 400 x = 16

3 x = x 64 - x^{2}

1.5 = 16.5 x^{- 1.38}

What is the answer to sqrt(4x-3)=2+sqrt(2x+5) ?
The answer to sqrt(4x-3)=2+sqrt(2x+5) is x=2(5+sqrt(21))
Solve for x: sqrt(4x-3)=2+sqrt(2x+5)
The solution is x=2(5+sqrt(21))