Solve for x
x = \frac{3 \sqrt{26}}{13} \approx 1.176696811
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3=\sqrt{\frac{13}{2}}x
Add 11 and 2 to get 13.
3=\frac{\sqrt{13}}{\sqrt{2}}x
Rewrite the square root of the division \sqrt{\frac{13}{2}} as the division of square roots \frac{\sqrt{13}}{\sqrt{2}}.
3=\frac{\sqrt{13}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}x
Rationalize the denominator of \frac{\sqrt{13}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.
3=\frac{\sqrt{13}\sqrt{2}}{2}x
The square of \sqrt{2} is 2.
3=\frac{\sqrt{26}}{2}x
To multiply \sqrt{13} and \sqrt{2}, multiply the numbers under the square root.
3=\frac{\sqrt{26}x}{2}
Express \frac{\sqrt{26}}{2}x as a single fraction.
\frac{\sqrt{26}x}{2}=3
Swap sides so that all variable terms are on the left hand side.
\sqrt{26}x=3\times 2
Multiply both sides by 2.
\sqrt{26}x=6
Multiply 3 and 2 to get 6.
\frac{\sqrt{26}x}{\sqrt{26}}=\frac{6}{\sqrt{26}}
Divide both sides by \sqrt{26}.
x=\frac{6}{\sqrt{26}}
Dividing by \sqrt{26} undoes the multiplication by \sqrt{26}.
x=\frac{3\sqrt{26}}{13}
Divide 6 by \sqrt{26}.
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