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

The answer to sqrt(x-2)=3-2sqrt(x) is x=(13-4sqrt(3))/3

Solve for x: sqrt(x-2)=3-2sqrt(x)

The solution is x=(13-4sqrt(3))/3

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x - 2 = 3 - 2 x

x = \frac{13 - 4 3}{3}

Decimal Notation

x = 2.02393 \dots

Solution steps

x - 2 = 3 - 2 x

Remove square roots

9 x^{2} + 66 x + 121 = 144 x

Solve

9 x^{2} + 66 x + 121 = 144 x : x = \frac{13 + 4 3}{3}, x = \frac{13 - 4 3}{3}

x = \frac{13 + 4 3}{3}, x = \frac{13 - 4 3}{3}

Verify Solutions:

x = \frac{13 + 4 3}{3}

False

, x = \frac{13 - 4 3}{3}

True

The solution is

x = \frac{13 - 4 3}{3}

(x^{2} + 45)^{\frac{1}{2}} = 7

2 = x + 1

x + x + 6 = 0

2 t + 7 = - 3

What is the answer to sqrt(x-2)=3-2sqrt(x) ?
The answer to sqrt(x-2)=3-2sqrt(x) is x=(13-4sqrt(3))/3
Solve for x: sqrt(x-2)=3-2sqrt(x)
The solution is x=(13-4sqrt(3))/3