Solve 2*4/x^2=0.8

$$\frac{ 2 \times 4 }{ { x }^{ 2 } } =0.8$$

Solve for x

$$x=\sqrt{10}\approx 3.16227766$$

$$x=-\sqrt{10}\approx -3.16227766$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.

$$2\times 4=0.8x^{2}$$

Multiply 2 and 4 to get 8.

$$8=0.8x^{2}$$

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

$$0.8x^{2}=8$$

Divide both sides by 0.8.

$$x^{2}=\frac{8}{0.8}$$

Expand \frac{8}{0.8} by multiplying both numerator and the denominator by 10.

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

Divide 80 by 8 to get 10.

$$x^{2}=10$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.

$$2\times 4=0.8x^{2}$$

Multiply 2 and 4 to get 8.

$$8=0.8x^{2}$$

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

$$0.8x^{2}=8$$

Subtract 8 from both sides.

$$0.8x^{2}-8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 0.8 for a, 0 for b, and -8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 0.8\left(-8\right)}}{2\times 0.8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 0.8\left(-8\right)}}{2\times 0.8}$$

Multiply -4 times 0.8.

$$x=\frac{0±\sqrt{-3.2\left(-8\right)}}{2\times 0.8}$$

Multiply -3.2 times -8.

$$x=\frac{0±\sqrt{25.6}}{2\times 0.8}$$

Take the square root of 25.6.

$$x=\frac{0±\frac{8\sqrt{10}}{5}}{2\times 0.8}$$

Multiply 2 times 0.8.

$$x=\frac{0±\frac{8\sqrt{10}}{5}}{1.6}$$

Now solve the equation x=\frac{0±\frac{8\sqrt{10}}{5}}{1.6} when ± is plus.

$$x=\sqrt{10}$$

Now solve the equation x=\frac{0±\frac{8\sqrt{10}}{5}}{1.6} when ± is minus.

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

The equation is now solved.

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