Solve 50=1/2(.05)x^2

$$50 = 1 / 2 ( .05 ) x ^ { 2 }$$

Solve for x

$$x=20\sqrt{5}\approx 44.72135955$$

$$x=-20\sqrt{5}\approx -44.72135955$$

Steps by Finding Square Root

Multiply \frac{1}{2} and 0.05 to get \frac{1}{40}.

$$50=\frac{1}{40}x^{2}$$

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

$$\frac{1}{40}x^{2}=50$$

Multiply both sides by 40, the reciprocal of \frac{1}{40}.

$$x^{2}=50\times 40$$

Multiply 50 and 40 to get 2000.

$$x^{2}=2000$$

Take the square root of both sides of the equation.

$$x=20\sqrt{5} x=-20\sqrt{5}$$

Steps Using the Quadratic Formula

Multiply \frac{1}{2} and 0.05 to get \frac{1}{40}.

$$50=\frac{1}{40}x^{2}$$

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

$$\frac{1}{40}x^{2}=50$$

Subtract 50 from both sides.

$$\frac{1}{40}x^{2}-50=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{40} for a, 0 for b, and -50 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{40}\left(-50\right)}}{2\times \frac{1}{40}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{1}{40}\left(-50\right)}}{2\times \frac{1}{40}}$$

Multiply -4 times \frac{1}{40}.

$$x=\frac{0±\sqrt{-\frac{1}{10}\left(-50\right)}}{2\times \frac{1}{40}}$$

Multiply -\frac{1}{10} times -50.

$$x=\frac{0±\sqrt{5}}{2\times \frac{1}{40}}$$

Multiply 2 times \frac{1}{40}.

$$x=\frac{0±\sqrt{5}}{\frac{1}{20}}$$

Now solve the equation x=\frac{0±\sqrt{5}}{\frac{1}{20}} when ± is plus.

$$x=20\sqrt{5}$$

Now solve the equation x=\frac{0±\sqrt{5}}{\frac{1}{20}} when ± is minus.

$$x=-20\sqrt{5}$$

The equation is now solved.

$$x=20\sqrt{5} x=-20\sqrt{5}$$