What is the answer to x/4 =sqrt(x+12) ?

The answer to x/4 =sqrt(x+12) is x=24

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x/4 =sqrt(x+12)

\frac{x}{4} = x + 12

x = 24

Solution steps

\frac{x}{4} = x + 12

Multiply both sides by

4

\frac{x}{4} \cdot 4 = x + 12 \cdot 4

Simplify

x = x + 12 \cdot 4

Square both sides:

x^{2} = 16 x + 192

x^{2} = 16 x + 192

Solve

x^{2} = 16 x + 192 : x = 24, x = - 8

x = 24, x = - 8

Verify Solutions:

x = 24

True

, x = - 8

False

The solution is

x = 24

n (x) = 3 x + \frac{4}{3}

16 + 6 x = x

1 + x + 3 = 2 x - 1

x, x^{\frac{3}{2}} = 8

4 - 4 x - 1 = - 16