Solve 54=2/3m^2

$$54 = \frac { 2 } { 3 } m ^ { 2 }$$

Solve for m

$$m=9$$

$$m=-9$$

Steps Using Difference of Squares

Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}.

$$54\times \frac{3}{2}=m^{2}$$

Multiply 54 and \frac{3}{2} to get 81.

$$81=m^{2}$$

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

$$m^{2}=81$$

Subtract 81 from both sides.

$$m^{2}-81=0$$

Consider m^{2}-81. Rewrite m^{2}-81 as m^{2}-9^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(m-9\right)\left(m+9\right)=0$$

To find equation solutions, solve m-9=0 and m+9=0.

$$m=9 m=-9$$

Steps by Finding Square Root

Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}.

$$54\times \frac{3}{2}=m^{2}$$

Multiply 54 and \frac{3}{2} to get 81.

$$81=m^{2}$$

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

$$m^{2}=81$$

Take the square root of both sides of the equation.

$$m=9 m=-9$$

Steps Using the Quadratic Formula

Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}.

$$54\times \frac{3}{2}=m^{2}$$

Multiply 54 and \frac{3}{2} to get 81.

$$81=m^{2}$$

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

$$m^{2}=81$$

Subtract 81 from both sides.

$$m^{2}-81=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -81 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\left(-81\right)}}{2}$$

Square 0.

$$m=\frac{0±\sqrt{-4\left(-81\right)}}{2}$$

Multiply -4 times -81.

$$m=\frac{0±\sqrt{324}}{2}$$

Take the square root of 324.

$$m=\frac{0±18}{2}$$

Now solve the equation m=\frac{0±18}{2} when ± is plus. Divide 18 by 2.

$$m=9$$

Now solve the equation m=\frac{0±18}{2} when ± is minus. Divide -18 by 2.

$$m=-9$$

The equation is now solved.

$$m=9 m=-9$$