Solve 8.2^2={left(x/4right)}^2+{left(x/4right)}^2

$${ 8.2 }^{ 2 } = { \left( \frac{ x }{ 4 } \right) }^{ 2 } + { \left( \frac{ x }{ 4 } \right) }^{ 2 }$$

Solve for x

$$x = \frac{82 \sqrt{2}}{5} \approx 23.193102423$$

$$x = -\frac{82 \sqrt{2}}{5} \approx -23.193102423$$

Steps by Finding Square Root

Calculate 8.2 to the power of 2 and get 67.24.

$$67.24=\left(\frac{x}{4}\right)^{2}+\left(\frac{x}{4}\right)^{2}$$

To raise \frac{x}{4} to a power, raise both numerator and denominator to the power and then divide.

$$67.24=\frac{x^{2}}{4^{2}}+\left(\frac{x}{4}\right)^{2}$$

To raise \frac{x}{4} to a power, raise both numerator and denominator to the power and then divide.

$$67.24=\frac{x^{2}}{4^{2}}+\frac{x^{2}}{4^{2}}$$

Combine \frac{x^{2}}{4^{2}} and \frac{x^{2}}{4^{2}} to get 2\times \frac{x^{2}}{4^{2}}.

$$67.24=2\times \frac{x^{2}}{4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$67.24=2\times \frac{x^{2}}{16}$$

Cancel out 16, the greatest common factor in 2 and 16.

$$67.24=\frac{x^{2}}{8}$$

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

$$\frac{x^{2}}{8}=67.24$$

Multiply both sides by 8.

$$x^{2}=67.24\times 8$$

Multiply 67.24 and 8 to get 537.92.

$$x^{2}=537.92$$

Take the square root of both sides of the equation.

$$x=\frac{82\sqrt{2}}{5} x=-\frac{82\sqrt{2}}{5}$$

Steps Using the Quadratic Formula

Calculate 8.2 to the power of 2 and get 67.24.

$$67.24=\left(\frac{x}{4}\right)^{2}+\left(\frac{x}{4}\right)^{2}$$

To raise \frac{x}{4} to a power, raise both numerator and denominator to the power and then divide.

$$67.24=\frac{x^{2}}{4^{2}}+\left(\frac{x}{4}\right)^{2}$$

To raise \frac{x}{4} to a power, raise both numerator and denominator to the power and then divide.

$$67.24=\frac{x^{2}}{4^{2}}+\frac{x^{2}}{4^{2}}$$

Combine \frac{x^{2}}{4^{2}} and \frac{x^{2}}{4^{2}} to get 2\times \frac{x^{2}}{4^{2}}.

$$67.24=2\times \frac{x^{2}}{4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$67.24=2\times \frac{x^{2}}{16}$$

Cancel out 16, the greatest common factor in 2 and 16.

$$67.24=\frac{x^{2}}{8}$$

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

$$\frac{x^{2}}{8}=67.24$$

Subtract 67.24 from both sides.

$$\frac{x^{2}}{8}-67.24=0$$

Multiply both sides of the equation by 8.

$$x^{2}-537.92=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -537.92 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-537.92\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-537.92\right)}}{2}$$

Multiply -4 times -537.92.

$$x=\frac{0±\sqrt{2151.68}}{2}$$

Take the square root of 2151.68.

$$x=\frac{0±\frac{164\sqrt{2}}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{164\sqrt{2}}{5}}{2} when ± is plus.

$$x=\frac{82\sqrt{2}}{5}$$

Now solve the equation x=\frac{0±\frac{164\sqrt{2}}{5}}{2} when ± is minus.

$$x=-\frac{82\sqrt{2}}{5}$$

The equation is now solved.

$$x=\frac{82\sqrt{2}}{5} x=-\frac{82\sqrt{2}}{5}$$