What is the answer to x/2 =sqrt(x/2+6) ?

The answer to x/2 =sqrt(x/2+6) is x=6

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x/2 =sqrt(x/2+6)

\frac{x}{2} = \frac{x}{2} + 6

x = 6

Solution steps

\frac{x}{2} = \frac{x}{2} + 6

Multiply both sides by

2

\frac{x}{2} \cdot 2 = \frac{x}{2} + 6 \cdot 2

Simplify

x = \frac{x}{2} + 6 \cdot 2

Square both sides:

x^{2} = 2 x + 24

x^{2} = 2 x + 24

Solve

x^{2} = 2 x + 24 : x = 6, x = - 4

x = 6, x = - 4

Verify Solutions:

x = 6

True

, x = - 4

False

The solution is

x = 6

2 y = 0

x + x^{\frac{3}{2}} - 2 x^{\frac{1}{2}} = 0

8 - x + 1 = x - 1

\frac{5}{4 x ^{\frac{3}{2}}} = 0

3 x^{2} - 6 = 5 3 x