Solve 16/64.2=x^2/18

$$\frac { 16 } { 64.2 } = \frac { x ^ { 2 } } { 18 }$$

Solve for x

$$x = \frac{4 \sqrt{3210}}{107} \approx 2.118013529$$

$$x = -\frac{4 \sqrt{3210}}{107} \approx -2.118013529$$

Steps by Finding Square Root

Multiply both sides of the equation by 18.

$$18\times \frac{16}{64.2}=x^{2}$$

Expand \frac{16}{64.2} by multiplying both numerator and the denominator by 10.

$$18\times \frac{160}{642}=x^{2}$$

Reduce the fraction \frac{160}{642} to lowest terms by extracting and canceling out 2.

$$18\times \frac{80}{321}=x^{2}$$

Multiply 18 and \frac{80}{321} to get \frac{480}{107}.

$$\frac{480}{107}=x^{2}$$

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

$$x^{2}=\frac{480}{107}$$

Take the square root of both sides of the equation.

$$x=\frac{4\sqrt{3210}}{107} x=-\frac{4\sqrt{3210}}{107}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 18.

$$18\times \frac{16}{64.2}=x^{2}$$

Expand \frac{16}{64.2} by multiplying both numerator and the denominator by 10.

$$18\times \frac{160}{642}=x^{2}$$

Reduce the fraction \frac{160}{642} to lowest terms by extracting and canceling out 2.

$$18\times \frac{80}{321}=x^{2}$$

Multiply 18 and \frac{80}{321} to get \frac{480}{107}.

$$\frac{480}{107}=x^{2}$$

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

$$x^{2}=\frac{480}{107}$$

Subtract \frac{480}{107} from both sides.

$$x^{2}-\frac{480}{107}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{480}{107} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{480}{107}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{480}{107}\right)}}{2}$$

Multiply -4 times -\frac{480}{107}.

$$x=\frac{0±\sqrt{\frac{1920}{107}}}{2}$$

Take the square root of \frac{1920}{107}.

$$x=\frac{0±\frac{8\sqrt{3210}}{107}}{2}$$

Now solve the equation x=\frac{0±\frac{8\sqrt{3210}}{107}}{2} when ± is plus.

$$x=\frac{4\sqrt{3210}}{107}$$

Now solve the equation x=\frac{0±\frac{8\sqrt{3210}}{107}}{2} when ± is minus.

$$x=-\frac{4\sqrt{3210}}{107}$$

The equation is now solved.

$$x=\frac{4\sqrt{3210}}{107} x=-\frac{4\sqrt{3210}}{107}$$