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16+\left(1+\frac{1}{6}\right)^{2}=x^{2}
Calculate 4 to the power of 2 and get 16.
16+\left(\frac{7}{6}\right)^{2}=x^{2}
Add 1 and \frac{1}{6} to get \frac{7}{6}.
16+\frac{49}{36}=x^{2}
Calculate \frac{7}{6} to the power of 2 and get \frac{49}{36}.
\frac{625}{36}=x^{2}
Add 16 and \frac{49}{36} to get \frac{625}{36}.
x^{2}=\frac{625}{36}
Swap sides so that all variable terms are on the left hand side.
x^{2}-\frac{625}{36}=0
Subtract \frac{625}{36} from both sides.
36x^{2}-625=0
Multiply both sides by 36.
\left(6x-25\right)\left(6x+25\right)=0
Consider 36x^{2}-625. Rewrite 36x^{2}-625 as \left(6x\right)^{2}-25^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
x=\frac{25}{6} x=-\frac{25}{6}
To find equation solutions, solve 6x-25=0 and 6x+25=0.
16+\left(1+\frac{1}{6}\right)^{2}=x^{2}
Calculate 4 to the power of 2 and get 16.
16+\left(\frac{7}{6}\right)^{2}=x^{2}
Add 1 and \frac{1}{6} to get \frac{7}{6}.
16+\frac{49}{36}=x^{2}
Calculate \frac{7}{6} to the power of 2 and get \frac{49}{36}.
\frac{625}{36}=x^{2}
Add 16 and \frac{49}{36} to get \frac{625}{36}.
x^{2}=\frac{625}{36}
Swap sides so that all variable terms are on the left hand side.
x=\frac{25}{6} x=-\frac{25}{6}
Take the square root of both sides of the equation.
16+\left(1+\frac{1}{6}\right)^{2}=x^{2}
Calculate 4 to the power of 2 and get 16.
16+\left(\frac{7}{6}\right)^{2}=x^{2}
Add 1 and \frac{1}{6} to get \frac{7}{6}.
16+\frac{49}{36}=x^{2}
Calculate \frac{7}{6} to the power of 2 and get \frac{49}{36}.
\frac{625}{36}=x^{2}
Add 16 and \frac{49}{36} to get \frac{625}{36}.
x^{2}=\frac{625}{36}
Swap sides so that all variable terms are on the left hand side.
x^{2}-\frac{625}{36}=0
Subtract \frac{625}{36} from both sides.
x=\frac{0±\sqrt{0^{2}-4\left(-\frac{625}{36}\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{625}{36} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\left(-\frac{625}{36}\right)}}{2}
Square 0.
x=\frac{0±\sqrt{\frac{625}{9}}}{2}
Multiply -4 times -\frac{625}{36}.
x=\frac{0±\frac{25}{3}}{2}
Take the square root of \frac{625}{9}.
x=\frac{25}{6}
Now solve the equation x=\frac{0±\frac{25}{3}}{2} when ± is plus.
x=-\frac{25}{6}
Now solve the equation x=\frac{0±\frac{25}{3}}{2} when ± is minus.
x=\frac{25}{6} x=-\frac{25}{6}
The equation is now solved.