Solve (2*2)divx^2=10

$$(2 \times 2) \div { x }^{ 2 } =10$$

Solve for x

$$x=\frac{\sqrt{10}}{5}\approx 0.632455532$$

$$x=-\frac{\sqrt{10}}{5}\approx -0.632455532$$

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}.

$$2\times 2=10x^{2}$$

Multiply 2 and 2 to get 4.

$$4=10x^{2}$$

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

$$10x^{2}=4$$

Divide both sides by 10.

$$x^{2}=\frac{4}{10}$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{2}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{10}}{5} x=-\frac{\sqrt{10}}{5}$$

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}.

$$2\times 2=10x^{2}$$

Multiply 2 and 2 to get 4.

$$4=10x^{2}$$

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

$$10x^{2}=4$$

Subtract 4 from both sides.

$$10x^{2}-4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, 0 for b, and -4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 10\left(-4\right)}}{2\times 10}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 10\left(-4\right)}}{2\times 10}$$

Multiply -4 times 10.

$$x=\frac{0±\sqrt{-40\left(-4\right)}}{2\times 10}$$

Multiply -40 times -4.

$$x=\frac{0±\sqrt{160}}{2\times 10}$$

Take the square root of 160.

$$x=\frac{0±4\sqrt{10}}{2\times 10}$$

Multiply 2 times 10.

$$x=\frac{0±4\sqrt{10}}{20}$$

Now solve the equation x=\frac{0±4\sqrt{10}}{20} when ± is plus.

$$x=\frac{\sqrt{10}}{5}$$

Now solve the equation x=\frac{0±4\sqrt{10}}{20} when ± is minus.

$$x=-\frac{\sqrt{10}}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{10}}{5} x=-\frac{\sqrt{10}}{5}$$