What is the answer to x/(2sqrt(x^2+25))-1/3 =0 ?

The answer to x/(2sqrt(x^2+25))-1/3 =0 is x=2sqrt(5)

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x/(2sqrt(x^2+25))-1/3 =0

\frac{x}{2 x ^{2} + 25} - \frac{1}{3} = 0

x = 25

Decimal Notation

x = 4.47213 \dots

Solution steps

\frac{x}{2 x ^{2} + 25} - \frac{1}{3} = 0

Find Least Common Multiplier of

2 x^{2} + 25, 3 : 6 x^{2} + 25

Multiply by LCM=

6 x^{2} + 25

\frac{x}{2 x ^{2} + 25} \cdot 6 x^{2} + 25 - \frac{1}{3} \cdot 6 x^{2} + 25 = 0 \cdot 6 x^{2} + 25

Simplify

3 x - 2 x^{2} + 25 = 0

Remove square roots

4 x^{2} + 100 = 9 x^{2}

Solve

4 x^{2} + 100 = 9 x^{2} : x = 25, x = - 25

x = 25, x = - 25

Verify Solutions:

x = 25

True

, x = - 25

False

The solution is

x = 25

1 + 3 x = x + 8 + 1

1 = \frac{x}{9 - x ^{2}}

15 - 2 x = 3

x + 2 2 x + 3 = 3

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

What is the answer to x/(2sqrt(x^2+25))-1/3 =0 ?
The answer to x/(2sqrt(x^2+25))-1/3 =0 is x=2sqrt(5)
Solve for x: x/(2sqrt(x^2+25))-1/3 =0
The solution is x=2sqrt(5)