Solve {left(4sqrt{5x^2}right)}^2=8

$${ \left(4 \sqrt{ 5 { x }^{ 2 } } \right) }^{ 2 } =8$$

Solve for x

$$x=\frac{\sqrt{10}}{10}\approx 0.316227766$$

$$x=-\frac{\sqrt{10}}{10}\approx -0.316227766$$

Steps by Finding Square Root

Expand \left(4\sqrt{5x^{2}}\right)^{2}.

$$4^{2}\left(\sqrt{5x^{2}}\right)^{2}=8$$

Calculate 4 to the power of 2 and get 16.

$$16\left(\sqrt{5x^{2}}\right)^{2}=8$$

Calculate \sqrt{5x^{2}} to the power of 2 and get 5x^{2}.

$$16\times 5x^{2}=8$$

Multiply 16 and 5 to get 80.

$$80x^{2}=8$$

Divide both sides by 80.

$$x^{2}=\frac{8}{80}$$

Reduce the fraction \frac{8}{80} to lowest terms by extracting and canceling out 8.

$$x^{2}=\frac{1}{10}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{10}}{10} x=-\frac{\sqrt{10}}{10}$$

Steps Using the Quadratic Formula

Expand \left(4\sqrt{5x^{2}}\right)^{2}.

$$4^{2}\left(\sqrt{5x^{2}}\right)^{2}=8$$

Calculate 4 to the power of 2 and get 16.

$$16\left(\sqrt{5x^{2}}\right)^{2}=8$$

Calculate \sqrt{5x^{2}} to the power of 2 and get 5x^{2}.

$$16\times 5x^{2}=8$$

Multiply 16 and 5 to get 80.

$$80x^{2}=8$$

Subtract 8 from both sides.

$$80x^{2}-8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 80 for a, 0 for b, and -8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 80\left(-8\right)}}{2\times 80}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 80\left(-8\right)}}{2\times 80}$$

Multiply -4 times 80.

$$x=\frac{0±\sqrt{-320\left(-8\right)}}{2\times 80}$$

Multiply -320 times -8.

$$x=\frac{0±\sqrt{2560}}{2\times 80}$$

Take the square root of 2560.

$$x=\frac{0±16\sqrt{10}}{2\times 80}$$

Multiply 2 times 80.

$$x=\frac{0±16\sqrt{10}}{160}$$

Now solve the equation x=\frac{0±16\sqrt{10}}{160} when ± is plus.

$$x=\frac{\sqrt{10}}{10}$$

Now solve the equation x=\frac{0±16\sqrt{10}}{160} when ± is minus.

$$x=-\frac{\sqrt{10}}{10}$$

The equation is now solved.

$$x=\frac{\sqrt{10}}{10} x=-\frac{\sqrt{10}}{10}$$