Solve 4^2+{left(1+1/6right)}^2=x^2

$${ 4 }^{ 2 } + { \left( 1+ \frac { 1 } { 6 } \right) }^{ 2 } = { x }^{ 2 }$$

Solve for x

$$x = \frac{25}{6} = 4\frac{1}{6} \approx 4.166666667$$

$$x = -\frac{25}{6} = -4\frac{1}{6} \approx -4.166666667$$

Steps Using Difference of Squares

Calculate 4 to the power of 2 and get 16.

$$16+\left(1+\frac{1}{6}\right)^{2}=x^{2}$$

Add 1 and \frac{1}{6} to get \frac{7}{6}.

$$16+\left(\frac{7}{6}\right)^{2}=x^{2}$$

Calculate \frac{7}{6} to the power of 2 and get \frac{49}{36}.

$$16+\frac{49}{36}=x^{2}$$

Add 16 and \frac{49}{36} to get \frac{625}{36}.

$$\frac{625}{36}=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=\frac{625}{36}$$

Subtract \frac{625}{36} from both sides.

$$x^{2}-\frac{625}{36}=0$$

Multiply both sides by 36.

$$36x^{2}-625=0$$

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).

$$\left(6x-25\right)\left(6x+25\right)=0$$

To find equation solutions, solve 6x-25=0 and 6x+25=0.

$$x=\frac{25}{6} x=-\frac{25}{6}$$

Steps by Finding Square Root

Calculate 4 to the power of 2 and get 16.

$$16+\left(1+\frac{1}{6}\right)^{2}=x^{2}$$

Add 1 and \frac{1}{6} to get \frac{7}{6}.

$$16+\left(\frac{7}{6}\right)^{2}=x^{2}$$

Calculate \frac{7}{6} to the power of 2 and get \frac{49}{36}.

$$16+\frac{49}{36}=x^{2}$$

Add 16 and \frac{49}{36} to get \frac{625}{36}.

$$\frac{625}{36}=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=\frac{625}{36}$$

Take the square root of both sides of the equation.

$$x=\frac{25}{6} x=-\frac{25}{6}$$

Steps Using the Quadratic Formula

Calculate 4 to the power of 2 and get 16.

$$16+\left(1+\frac{1}{6}\right)^{2}=x^{2}$$

Add 1 and \frac{1}{6} to get \frac{7}{6}.

$$16+\left(\frac{7}{6}\right)^{2}=x^{2}$$

Calculate \frac{7}{6} to the power of 2 and get \frac{49}{36}.

$$16+\frac{49}{36}=x^{2}$$

Add 16 and \frac{49}{36} to get \frac{625}{36}.

$$\frac{625}{36}=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=\frac{625}{36}$$

Subtract \frac{625}{36} from both sides.

$$x^{2}-\frac{625}{36}=0$$

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}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{625}{36}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{625}{36}\right)}}{2}$$

Multiply -4 times -\frac{625}{36}.

$$x=\frac{0±\sqrt{\frac{625}{9}}}{2}$$

Take the square root of \frac{625}{9}.

$$x=\frac{0±\frac{25}{3}}{2}$$

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.

$$x=-\frac{25}{6}$$

The equation is now solved.

$$x=\frac{25}{6} x=-\frac{25}{6}$$