Solve 1^2/4x=5x

$$\frac { 1 ^ { 2 } } { 4 x } = 5 x$$

Solve for x

$$x=\frac{\sqrt{5}}{10}\approx 0.223606798$$

$$x=-\frac{\sqrt{5}}{10}\approx -0.223606798$$

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 4x.

$$1^{2}=5x\times 4x$$

Calculate 1 to the power of 2 and get 1.

$$1=5x\times 4x$$

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

$$1=5x^{2}\times 4$$

Multiply 5 and 4 to get 20.

$$1=20x^{2}$$

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

$$20x^{2}=1$$

Divide both sides by 20.

$$x^{2}=\frac{1}{20}$$

Take the square root of both sides of the equation.

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

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 4x.

$$1^{2}=5x\times 4x$$

Calculate 1 to the power of 2 and get 1.

$$1=5x\times 4x$$

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

$$1=5x^{2}\times 4$$

Multiply 5 and 4 to get 20.

$$1=20x^{2}$$

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

$$20x^{2}=1$$

Subtract 1 from both sides.

$$20x^{2}-1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 20 for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 20\left(-1\right)}}{2\times 20}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 20\left(-1\right)}}{2\times 20}$$

Multiply -4 times 20.

$$x=\frac{0±\sqrt{-80\left(-1\right)}}{2\times 20}$$

Multiply -80 times -1.

$$x=\frac{0±\sqrt{80}}{2\times 20}$$

Take the square root of 80.

$$x=\frac{0±4\sqrt{5}}{2\times 20}$$

Multiply 2 times 20.

$$x=\frac{0±4\sqrt{5}}{40}$$

Now solve the equation x=\frac{0±4\sqrt{5}}{40} when ± is plus.

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

Now solve the equation x=\frac{0±4\sqrt{5}}{40} when ± is minus.

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

The equation is now solved.

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