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

The answer to solvefor x,sqrt(x-4)+5=sqrt(3x+3) is x=(43+15sqrt(5))/2

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solvefor x,sqrt(x-4)+5=sqrt(3x+3)

x, x - 4 + 5 = 3 x + 3

x = \frac{43 + 15 5}{2}

Decimal

x = 38.27050 \dots

Solution steps

x - 4 + 5 = 3 x + 3

Remove square roots

100 x - 400 = 4 x^{2} - 72 x + 324

Solve

100 x - 400 = 4 x^{2} - 72 x + 324 : x = \frac{43 + 15 5}{2}, x = \frac{43 - 15 5}{2}

x = \frac{43 + 15 5}{2}, x = \frac{43 - 15 5}{2}

Verify Solutions:

x = \frac{43 + 15 5}{2}

True

, x = \frac{43 - 15 5}{2}

False

The solution is

x = \frac{43 + 15 5}{2}

x - 3 = x - 6

x - 3 = x - 3

5 x + 29 + 6 = 2 x

x + 3 - 7 - x = 2

3 x + 7 = x + 9

What is the answer to solvefor x,sqrt(x-4)+5=sqrt(3x+3) ?
The answer to solvefor x,sqrt(x-4)+5=sqrt(3x+3) is x=(43+15sqrt(5))/2