Solve 5/2x=20quad10x/2

$$\frac { 5 } { 2 x } = 20 \quad \frac { 10 x } { 2 }$$

Solve for x

$$x=\frac{\sqrt{10}}{20}\approx 0.158113883$$

$$x=-\frac{\sqrt{10}}{20}\approx -0.158113883$$

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 2x, the least common multiple of 2x,2.

$$5=20x\times 10x$$

Multiply x and x to get x^{2}.

$$5=20x^{2}\times 10$$

Multiply 20 and 10 to get 200.

$$5=200x^{2}$$

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

$$200x^{2}=5$$

Divide both sides by 200.

$$x^{2}=\frac{5}{200}$$

Reduce the fraction \frac{5}{200} to lowest terms by extracting and canceling out 5.

$$x^{2}=\frac{1}{40}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{10}}{20} x=-\frac{\sqrt{10}}{20}$$

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 2x, the least common multiple of 2x,2.

$$5=20x\times 10x$$

Multiply x and x to get x^{2}.

$$5=20x^{2}\times 10$$

Multiply 20 and 10 to get 200.

$$5=200x^{2}$$

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

$$200x^{2}=5$$

Subtract 5 from both sides.

$$200x^{2}-5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 200 for a, 0 for b, and -5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 200\left(-5\right)}}{2\times 200}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 200\left(-5\right)}}{2\times 200}$$

Multiply -4 times 200.

$$x=\frac{0±\sqrt{-800\left(-5\right)}}{2\times 200}$$

Multiply -800 times -5.

$$x=\frac{0±\sqrt{4000}}{2\times 200}$$

Take the square root of 4000.

$$x=\frac{0±20\sqrt{10}}{2\times 200}$$

Multiply 2 times 200.

$$x=\frac{0±20\sqrt{10}}{400}$$

Now solve the equation x=\frac{0±20\sqrt{10}}{400} when ± is plus.

$$x=\frac{\sqrt{10}}{20}$$

Now solve the equation x=\frac{0±20\sqrt{10}}{400} when ± is minus.

$$x=-\frac{\sqrt{10}}{20}$$

The equation is now solved.

$$x=\frac{\sqrt{10}}{20} x=-\frac{\sqrt{10}}{20}$$