What is the answer to 2+sqrt(x-1)= x/2 ?

The answer to 2+sqrt(x-1)= x/2 is x=10

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

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

x = 10

Solution steps

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

Multiply both sides by

2

2 \cdot 2 + x - 1 \cdot 2 = \frac{x}{2} \cdot 2

Simplify

4 + 2 x - 1 = x

Remove square roots

4 x - 4 = x^{2} - 8 x + 16

Solve

4 x - 4 = x^{2} - 8 x + 16 : x = 10, x = 2

x = 10, x = 2

Verify Solutions:

x = 10

True

, x = 2

False

The solution is

x = 10

5 - 2 x = 2 x - 3

x + 5 - x - 4 = 1

2 - 7 x + 2 x = 0

x = 2 x 25 - x^{2}