Solve 75/x=12,5/0,5quadx=

$$\frac { 75 } { x } = \frac { 12,5 } { 0,5 } \quad x =$$

Solve for x

$$x=\sqrt{3}\approx 1.732050808$$

$$x=-\sqrt{3}\approx -1.732050808$$

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.

$$75=2x\times 12,5x$$

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

$$75=2x^{2}\times 12,5$$

Multiply 2 and 12,5 to get 25.

$$75=25x^{2}$$

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

$$25x^{2}=75$$

Divide both sides by 25.

$$x^{2}=\frac{75}{25}$$

Divide 75 by 25 to get 3.

$$x^{2}=3$$

Take the square root of both sides of the equation.

$$x=\sqrt{3} x=-\sqrt{3}$$

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.

$$75=2x\times 12,5x$$

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

$$75=2x^{2}\times 12,5$$

Multiply 2 and 12,5 to get 25.

$$75=25x^{2}$$

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

$$25x^{2}=75$$

Subtract 75 from both sides.

$$25x^{2}-75=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 25 for a, 0 for b, and -75 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 25\left(-75\right)}}{2\times 25}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 25\left(-75\right)}}{2\times 25}$$

Multiply -4 times 25.

$$x=\frac{0±\sqrt{-100\left(-75\right)}}{2\times 25}$$

Multiply -100 times -75.

$$x=\frac{0±\sqrt{7500}}{2\times 25}$$

Take the square root of 7500.

$$x=\frac{0±50\sqrt{3}}{2\times 25}$$

Multiply 2 times 25.

$$x=\frac{0±50\sqrt{3}}{50}$$

Now solve the equation x=\frac{0±50\sqrt{3}}{50} when ± is plus.

$$x=\sqrt{3}$$

Now solve the equation x=\frac{0±50\sqrt{3}}{50} when ± is minus.

$$x=-\sqrt{3}$$

The equation is now solved.

$$x=\sqrt{3} x=-\sqrt{3}$$